I will review recent progress on deformations of string sigma-models. I will focus in particular on a class called 'homogeneous Yang-Baxter deformations' which can be understood as generalisations of TsT deformations, when the algebra of isometries participating in the deformation is non-abelian. Many features of TsT can be extended to Yang-Baxter, including the fact that they can be understood as solution-generating techniques in supergravity via the O(D,D)-covariant language of Double Field Theory. This reformulation, actually, makes it also manifest that Yang-Baxter deformations admit consistent alpha'-corrections at least at the first order (in the bosonic and heterotic string). When it comes to integrability, we can exploit the fact that, as for TsT, a Yang-Baxter deformed sigma-model is equivalent on-shell to an undeformed model with twisted boundary conditions. In the Yang-Baxter case the twisted boundary conditions involve complicated non-linear relations, though. I will review this construction and argue that it is a starting point to extend the integrability methods to these deformed models, which can be studied also as integrable deformations of AdS/CFT.

The recent CDF measurement of the W-boson mass draws new attention to global analyses of the Standard Model Effective Field Theory (SMEFT), an approach to constraining new physics in a model-independent way. However, present global analyses that only include high-energy observables predict a large, percent-level, violation of first-row CKM unitarity. We point out the necessity to consider low-energy observables, such as the beta-decay, in resolutions of the W mass anomaly in SMEFT that go beyond pure oblique corrections. We discuss the flat directions in SMEFT that are being lifted after including beta-decay constraints, and investigate what solutions to the W mass anomaly are still viable.

Recent progress in understanding QCD at the perturbative level led to the possibility to perform precision studies at lepton and even hadron colliders that go well beyond of what was considered possible earlier. Given this remarkable progress a question about possible non-perturbative effects and their impact on precision collider observables becomes relevant. In this talk I will discuss a few examples where improved understanding of non-perturbative effecs in collider physics would be desirable, and describe early attempts to make progress in this direction.

The classical double copy relates specific solutions in gauge theories to their gravitational counterparts which, under certain conditions, can be related to on-shell three-particle scattering amplitudes. In this talk, I will discuss how certain classical curvature spinors in topologically massive gauge theories and gravity can inherit the double copy from the underlying three-particle amplitudes resulting in the Cotton double copy, a three-dimensional cousin of the Weyl double copy.

The doubled formulation of the worldsheet provides a description of string theory in which T-duality is promoted to a manifest symmetry. I will discuss the extension of doubled formulation to N=(2,2) superspace thus providing a doubled formulation for bi-Hermitian/generalised Kähler target spaces. The dynamics of a doubled model is concisely described by a single function, a doubled-generalised Kähler potential, supplemented with a manifestly N=(2,2) constraint. The developed formalism will be applied to concrete examples.

We discuss the calculation of Einstein-Yang-Mills scattering amplitudes at one-loop level and multiplicity five using generalised unitarity cuts in D = 4 – 2 epsilon dimensions. More specifically, we will go through the computation of the all-plus helicity configuration with four gluons and one graviton.

We will review a recent application of Exceptional Field Theory: finding new families of solutions of type IIB supergravity on AdS_4 x S^1 x S^5. To find such solutions, we will compactify type IIB on S^5 x S^1 to obtain a 4d gauged maximal supergravity where new solutions are simply found by extremizing a scalar potential. Surprisingly, it is sometime possible to deform our new solutions and break any residual supersymmetry while preserving stability. This is surprising since, from a holographic perspective, these deformations should be dual to non-supersymmetric exactly marginal deformations. We will show that it is a generic behaviour of gravity theories compactified on a circle and we will provide a solution generating technique in terms of a tool called the mapping torus.

Merging neutron stars are a source of detected gravitational waves on earth. This gives rise to an interest in the description of tidal effects in the scattering of two massive bodies of finite size. This thesis extends a WQFT in Post-Minkowskian expansion describing bodies as point masses to quadrupole tidal effects. We use this to provide a correction in LO to the wave form and look at its impact on radiative effects on the deflection. Furthermore we provide a correction to conservative deflection and Eikonal up to NLO.

Recent years have seen a renewed interest in analytical treatments of the dissipative two body problem in gravity. This is mainly due to the recent detections of gravitational waves by LIGO and VIRGO from binary coalescences. The inspiral phase, the initial phase of the coalescence event where the typical velocities of the binary system are small and the constituents are largely separated, is subject to an analytic Post-Newtonian (PN) perturbative treatment. Lately, many tools originating from particle physics and QFT have been utilized for the analytic solution of the problem such as EFT methods and modern methods for Scattering Amplitudes both for the PN and the fully relativistic Post-Minkowskian (PM) regime. In this seminar, we will review some of the recent advances of this newborn subfield and focus on specific contributions of the speaker.

In this talk I will discuss an integrable bootstrap framework for the computation of correlation functions in beta-deformed N=4 SYM and introduce a beta-deformed hexagon form factor. After discussing the hexagon program, I am going to present some explicit checks using three-point functions. This talk is based on work with Burkhard Eden, Tristan McLoughlin, Fiona Seibold, Alessandro Sfondrini and Anne Spiering.

Accurate waveform models are crucial for gravitational-wave data analysis, and since numerical-relativity waveforms are computationally expensive, it is important to improve the analytical description of the binary dynamics. The post-Newtonian (PN) approximation is valid for small velocities and weak gravitational field, while the post-Minkowskian (PM) approximation is valid for arbitrary velocities in the weak field. We assess the accuracy of recent results for the 4PM conservative dynamics through comparisons with the PN approximation and numerical relativity simulations for the circular-orbit binding energy and the scattering angle. We also incorporate the PM results in effective-one-body Hamiltonians, which significantly improves the accuracy over PM-expanded Hamiltonians. We find that while the 4PM approximation gives comparable results to the 3PN approximation for bound orbits, it performs better for scattering encounters.

We introduce a class of bialgebras that formalizes the properties of bialgebras that appear naturally in topology, number theory and physics. We give the obstruction to the existence of antipodes for these algebras using a Takeuchi/Quillen type of setup. In renormalization the antipodes are used to construct involution inverses for arbitrary characters. More generally, we can give conditions on characters, such that their convolution inverse exists. These restricted characters factor through universal quotients and lift to quantum deformations.

In this talk I will present how the 1d CFT defined by the half-BPS Wilson line in planar N=4 super Yang-Mills can be solved in a perturbative expansion around strong coupling using analytic bootstrap methods. I will also comment on how the results obtained in this way reproduce the available data from integrability-based methods. The talk is based on joint work with Pietro Ferrero.

We consider the space of supersymmetric AdS5 solutions of type IIB supergravity corresponding to the conformal manifold of the dual 4d N = 1 conformal field theories. We describe how the background geometry naturally encodes a holomorphic generalised structure, dual to the superpotential of the field theory. Using this generalised language, we address the long-standing problem of finding the gravity duals of the generic N = 1 deformations of N = 4 super Yang-Mills: though we are not able to give it in a fully explicit form, we provide a proof-of-existence of the supergravity solutions. Using this formalism, we analyse the moduli of these supergravity backgrounds and derive a new result for the Hilbert series of the deformed field theories.

Results in Quantum Field Theories, such as anomalous dimensions or scattering amplitudes are known to exhibit rich properties under the Galois coaction that acts on period integrals. I will show how these phenomena arise directly from an integrability setup describing the anomalous dimensions of an integrable four-dimensional scalar model. I will also discuss a conjectural all-loop differential equation containing derivatives with respect to Riemann zeta values.

In this talk I will describe constraints from causality and unitarity on 2->2 graviton scattering in weakly-coupled gravitational effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, I will explain how to derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Such bounds imply that gravitational interactions must shut off uniformly in the limit G->0, and prove the scaling with M expected from dimensional analysis. In addition they demonstrate the gravity must be weakly coupled at all scales below Planck. Time permitting, I will comment on the experimental implications of the bounds.

Supergravity brane solutions provide a variety of contexts for effectively obtaining lower-dimensional physics within a higher-dimensional theory, but with noncompact transverse spaces instead of a usual Kaluza-Klein compactification. Two such contexts will be discussed. One is a promotion of the static “vacuum” brane solution to a full braneworld supergravity theory for the degree of supersymmetry possessed by the static brane. This allows for a “consistent truncation” brane supergravity ansatz in which the vacuum brane serves as a standard “skeleton” for embedding in the higher dimensional theory. The second is a more complete localization which exists in situations where the transverse wave equation spectrum starts with a normalizable zero mode state separated by a mass gap from the continuum expected in a noncompact transverse space. An example based on a transverse Eguchi-Hanson space will be given.

I will review a number of geometric approaches to understanding properties of scattering amplitudes. In particular we will discuss the relation of the geometry of the kinematical space to the analytic behaviour of amplitudes as functions on this space. Our focus will be on massless scattering amplitudes with N=4 super Yang-Mills theory as a guiding example, where cluster algebras of Grassmannian spaces play a central role.

We will present recent progress in the classification and construction of supersymmetric AdS(3) solutions in String Theory. This includes the classification of minimally supersymmetric solutions, and the construction of large families of N=(2,0) supersymmetric AdS(3) solutions in massive Type IIA supergravity. We will also discuss N=(2,2) supersymmetric AdS(3) solutions arising from D3-branes on Riemann surfaces of constant, as well as non-constant curvature.

After a short introduction on conformal branes in WZW models I will discuss the study of integrable brane configurations embedded in lambda-deformations. Then, I will focus on integrable branes embedded in a class of models known as generalized lambda-deformations which appear as multi-parametric deformations of a product of WZW models and interpolate between two exact CFTs in the UV and IR fixed points.

D-branes will be introduced in the framework of doubled geometry as conformal boundary conditions for the open string formulation of the Born sigma-model. This suggests a general characterisation of such D-branes as maximally isotropic subbundles on a para-Hermitian manifold. In particular, the reduction procedure of the D-branes to the physical spacetime will be tackled by describing them as Dirac structures. Furthermore a comparison with generalised complex branes will be drawn by defining their para-complex counterpart.

Recently, powerful quantum field theory techniques, originally developed to calculate observables in colliders, have been applied to describe classical observables relevant to gravitational wave physics. This has motivated a proliferation of approaches to extract classical information from quantum scattering amplitudes. Since the double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory, in this talk I will first discuss scattering in Yang-Mills theory as a toy model to study the connection between the framework by Kosower-Maybee-O'Connell (KMOC), the language of effective field theory (EFT) and the eikonal phase. After a brief review of the KMOC formalism to compute classical observables from scattering amplitudes, I will consider the dynamics of colour-charged particle scattering and explain how to compute the change of colour, and the radiation of colour, during a classical collision. Finally, moving on to gravity, I will discuss the deflection of light by a massive spinless/spinning object using the novel worldline quantum field theory (WQFT) formalism for classical scattering.

The factorial divergence of perturbative expansions is believed to be governed by two seemingly unrelated phenomena: Instantons that arise due to nontrivial solutions of the classical field equations and renormalons that appear due to a factorially growing contribution from the renormalization subtraction terms of a family of Feynman diagrams. I will report on joint work with David Broadhurst, Gerald Dunne and Max Meynig in which a particularly interesting renormalon in phi^3 theory was analyzed using tools from Ecalle's resurgence framework. A recent work with David Broadhurst revealed the intricate role of 'resonant' logarithmic terms for this renormalon and allowed an all-trans-series-order resurgence analysis. The overall shape of our all-order trans-series solution and our (well-tested) conjectured formulas for the asymptotic behaviour of the trans-series coefficients hint at the existence of a reality cancellation mechanism as it is observed in quantum mechanical instanton computations.

Generalisations of T- and U-duality have a natural description using doubled and exceptional geometry. In the former case, non-Abelian T-duality (NATD) in particular has proven to be of great use as a technique to generate new (holographic) supergravity solutions in 10 dimensions. This talk will describe some first steps towards finding similar solutions in 11 dimensions based on structures analogous to those present in non-Abelian T-dual solutions, in particular the presence of dual 3-algebra (rather than Lie algebra) structure constants, encoded in a trivector (rather than a bivector). Starting with brane intersecting solutions in type IIA I will generate a new 11-dimensional solution, describe how its AdS limit fits into a class of already NATD-inspired M-theory AdS_3 solutions, and discuss the appearance of an additional E6-valued six-vector deformation. Based on upcoming work with Sofia Zhidkova and previous work https://arxiv.org/abs/2006.12452 with Dan Thompson and Sofia Zhidkova.

Numerical calculations of lattice regularized QFTs are a powerful tool to understand such theories when analytic methods are not applicable. However, the utility of numerical results can be affected by two issues: (i) calculations are necessarily performed in a finite-volume spacetime and (ii) Euclidean (rather than Minkowski) signature correlation functions are evaluated. Both aspects play an especially important role for multi-particle observables including scattering and decay amplitudes and inclusive rates. In this colloquium, I will discuss progress for extracting such observables from numerical lattice field theory based on two strategies. One is to use the finite-volume as a tool, rather than an unwanted artefact, and to apply generic field theoretic relations between finite-volume quantities and infinite-volume amplitudes. The second is to carefully regulate the inverse Laplace transform, in order to estimate Minkowski observables directly from numerical Euclidean correlators.

Knowledge about the symmetries of a physical system can help finding the solution of the system, e.g. radial symmetry for a charge density or periodicity in solids. But it also makes sense to study models with a large number of symmetries not manifest in physical reality. Those models lend themeselves to a rich field of mathematics and physics, as they allow us to find explicit results not available in models close to reality. In my master's thesis I study such quantum field theory, namely N=4 Super Yang-Mills theory with Wilson-line defect, as it is suitable for the study of conformal and supersymmetry. I will show you the progress I have made so far in the calculation of a correlator of four operator insertions on the Wilson-line using superconformal bootstrap methods as well as explicit perturbative computations. This approach both exploits the strong constraints from symmetry and the computability of perturbation theory. I will point out some peculiarities of the one-loop computation, as well as checks of my results coming from conformal symmetry.

We consider multi-edge or banana graphs bn on n internal edges with different masses. We focus on the cut banana graphs from which the full result can be derived through dispersion. We give a recursive definition of the cut graph amplitude through iterated integrals. We discuss the structure of this iterated integral in detail. A discussion of accompanying differential equations, of monodromy and of a basis of master integrals is included.

In this talk I will explain the relation between Calabi-Yau manifolds and their mathematics and Feynman integral computations. We will see how concepts from Calabi-Yau geometries and especially Calabi-Yau motives can be used to compute multi-loop Feynman integrals. This will be exemplified with the so called banana graphs. First, I will give a short introduction to Feynman integrals and Calabi-Yau manifolds. Then we will see how the mathematics of Calabi-Yau manifolds (variations of Hodge structures, Griffiths transversality, Gammaclass, ...) constrain or even determine the corresponding Feynman integrals, here the banana graphs. Then I will also shortly comment on banana integrals in dimensional regularization. Finally, I will make some remarks what we can in general learn from Calabi-Yau spaces in the context of Feynman integrals.

The topological A/B-model have been important tools for studying both string theory and the geometry of Calabi-Yau manifolds. They provide both new geometric invariants of the Calabi-Yau, as well as calculating certain terms in the effective theory of string theory. While topological strings on other special holonomy manifolds have been postulated, they are far less understood. In my talk, I will examine the topological string on G2 and Spin(7) manifolds from the target space perspective. I will show that any special holonomy manifold has a double complex which generalises the Dolbeault complex of Calabi-Yau manifolds and provides the natural candidate for the BRST complex of the topological string. Through this, I will be able to conjecture the cohomology of operators and the 1-loop partition functions of the G2 and Spin(7) topological strings.

One dimensional CFTs are an exceptional laboratory in which we can test novel techniques in order to solve higher dimensional CFTs. They are also relevant from an holographic point of view, as in the case of conformal line defects in 4d N=4 Super Yang-Mills. In this talk, I will present a recursive prescription to compute, up to one loop, 4d N=4 SYM n-point correlation functions realised inserting protected operators on a 1/2-BPS Wilson line. Interestingly, these correlators are annihilated by a special class of differential operators, that can be considered as a multipoint extension of the superconformal Ward identities satisfied by the four-point functions.

We present a blueprint, named Caesar, for the numerical evaluation of Feynman integrals that substantially improves the accuracy and computing time compared to other general numerical methods, while being flexible enough for a large class of applications in electroweak precision physics, Higgs physics, flavor physics and elsewhere. The launch of the project Caesar is directly correlated to the computations of the three-loop corrections contributing to the pseudo observables which are well defined at the Z-boson resonance. I will give a short motivation why this is important for the studies involving the future e+e- colliders like CEPC, ILC and FCC-ee.

Scattering amplitudes of elementary particles exhibit a fascinating simplicity, which is entirely obscured in textbook Feynman-diagram computations. While these quantities find their primary application to collider physics, describing the dynamics of the tiniest particles in the universe, they also characterise the interactions among some of its heaviest objects, such as black holes. Violent collisions among black holes occur where tremendous amounts of energy are emitted, in the form of gravitational waves. 100 years after having been predicted by Einstein, their extraordinary direct detection in 2015 opened a fascinating window of observation of our universe at extreme energies never probed before, and it is now crucial to develop novel efficient methods for highly needed high-precision predictions. Thanks to their inherent simplicity, amplitudes are ideally suited to this task. I will begin by reviewing the computation of a very familiar quantity Newton’s potential, from scattering amplitudes and unitarity. I will then explain how to compute directly observable quantities such as the scattering angle for light or for gravitons passing by a heavy mass such as a black hole. These computations are further simplified thanks to a remarkable, yet still mysterious connection between scattering amplitudes of gluons (in Yang-Mills theory) and those of gravitons (in Einstein’s General relativity), known as the “double copy”, whereby the latter amplitudes can be expressed, schematically, as sums of squares of the former — a property that cannot be possibly guessed by simply staring at the Lagrangians of the two theories. I will conclude by discussing the prospects of performing computations in Einstein gravity to higher orders in Newton’s constant using a new, gauge-invariant version of the double copy, and as an example I will briefly discuss the computation of the scattering angle for classical black hole scattering to third post-Minkowskian order (or O(G^3) in Newton’s constant G).

In the light of recently reported discrepancies between data and theory for the ttW normalization in either ttH measurements or tttt searches in the multilepton channels the accurate modelling of these complex signatures is revisited. I will discuss the current status of the modelling of ttW signatures from full off-shell NLO QCD predictions to parton shower matched calculations and point our the dominant theory uncertainties in both approaches. Furthermore, I will present a comparison of both approaches to highlight differences in the description of fiducial signatures.

Since the start of the century the behaviour of the gluon and ghost propagators have been widely studied on the lattice at low momenta. In the Landau gauge the gluon propagator freezes to a non-zero finite value indicating the presence of a mass scale. Such a scale could be explained from a field theory point of view via the Gribov construction. Work by Serreau and Tissier showed that the effect of Gribov copies could be modeled by the inclusion of a gluon mass operator in Yang-Mills theory which effectively plays a role of an additional gauge parameter. By computing the gluon and ghost propagators in Yang-Mills to two loops it was previously shown that the lattice propagators could be fitted extremely well over the full momentum range. This talk concentrates on the extension of that work to include massive quarks. One goal is to probe how far the perturbative approximation can be relied upon when the physical limit is taken on the lattice for the quark mass function. A two loop computation is necessary in order to accommodate the interplay between the quark and gluon mass scales. For instance the behaviour of the quark dressing function cannot be accommodated by a one loop fit; a two loop fit is required.

I will start by reviewing the physics of KK bubbles and their higher-dimensional generalizations. Secondly, I will move to discussing slightly more general situations where the shrinking modulus is the string coupling. Subsequently I will focus on cases where a Freund-Rubin flux is present, thus leading to the necessity of introducing a source. Finally, I will discuss the case of massive IIA on a 6-sphere as an explicit realization of the aforementioned mechanism and provide an appropriate physical interpretation.

In the realm of AdS/CFT correspondence, integrable deformations open up a field of new integrable theories. A well-studied group of such deformations is spanned by the Yang-Baxter deformations of the AdS5xS5 string, which result in Drinfel’d twists of the underlying symmetry algebra. On the field theory side, this can lead to so called non-commutative field theories. This drastically change the gauge symmetry of the theory. I will explicitly show, how to derive gauge invariant actions as a deformation of N=4 SYM and how to recover gauge symmetry for a specific Drinfel’d twist. I will construct gauge invariant operators and show how to map their two point functions to their undeformed counterparts.

Finding master integrals of uniform weight is an essential step in computing Feynman integrals. It is well-known that constant leading singularities and maximal cuts provide helpful information for this task. Based on these concepts I describe a heuristic method, which turns this problem for non-trivial situations into an back-of-the-envelope calculation. I illustrate the method with a two-loop penguin diagram. Zoom password upon request.

The Kerr spacetime is said to possess hidden symmetry, not corresponding to any spacetime isometry, responsible for the integrability of geodesic motion and the separability of various wave equations on a Kerr background. It was also shown by Rüdiger to imply the existence of two (extra) hidden constants of motion (in addition to those due to Killing symmetries, and quantities conserved in any background) for a spinning test body in Kerr, governed by the Mathisson-Papapetrou-Dixon equations, up to the dipole order in the test body's multipole expansion, through linear order in its spin. (This was independently rediscovered in a supersymmetric guise by Gibbons et al. in 'SUSY in the sky.') This was shown by Witzany to be related to the separability of a Hamilton-Jacobi equation for the pole-dipole system in Kerr. We demonstrate that Witzany's construction leads to a gauge-invariant radial action integral for scattering orbits --- a function only of the constants of motion, for generic (precessing) spin orientations --- which is closely related to the eikonal phase function derived from the relevant relativistic quantum scattering amplitude, in the classical limit, and in the (spinning) probe limit. We find generalizations of Rüdiger's constants to the quadrupole level, through quadratic order in the test spin, for the specific case of an effective (quadrupolar) spinning test black hole in a Kerr background. We note a dependence only on these and the other constants of motion (for two copies of the multipolar-test-body limit, with the black holes' identities exchanged), in the eikonal phase derived from scattering amplitudes conjectured to describe generic binary black hole scattering through 1-loop (second post-Minkowskian) order and through quartic order in the black hole spins, as recently worked out by Chen, Chung, Huang and Kim.

In the paper 'Quantization of gauge fields, graph polynomials and graph cohomology' Dirk Kreimer, Matthias Sars and Walter van Suijlekom introduced two variants of graph homology to encode consistency conditions in the quantization of non-abelian gauge theories. One of their main results states that the combinatorial Green's function is a cycle in a big total complex built out of certain complexes of graphs (it is in fact also closed, and represents the only homology class of this complex). In this talk I will give a quick review of the relevant chain complexes of marked graphs, then show how to proof the latter statement using a simple universal model of such complexes (this was joint work with Andre Knispel). These simple model complexes are actually well-known in a rather unrelated field of discrete mathematics; they are (double complexes associated to) the simplicial chain complexes of independence complexes of graphs. I will explain what these are, how the connection works and how it gives a new method to study the homology of independence complexes.

In the past years the double copy prescription has allowed to significantly simplify the computation of gravity scattering amplitudes starting from gauge theory ones. Even more importantly, the double copy structure of gravity amplitudes has revealed a surprisingly simple connection between the two theories, gravity and Yang-Mills, which is greatly hidden in their Lagrangian formulation. In this talk I will employ the worldline formalism, as well as tools borrowed from String Field Theory, to elucidate how the double copy is implemented at the Lagrangian level. In particular, I will provide a simple doubling prescription which generates the quadratic Lagrangian of Double Field Theory starting from the free Maxwell action.

The CP structure of the Higgs boson in its coupling to the particles of the Standard Model is amongst the most important Higgs boson properties which have not yet been constrained with high precision. In this talk, I will explain how existing inclusive and differential Higgs boson measurements from the ATLAS and CMS experiments can be used to constrain the CP nature of the top-Yukawa interaction. Moreover, I will show how machine-learning-based inference can be used to tighten these constraints in the future by exploiting the full kinematic information. At the end of the talk, I will also shortly discuss the constraints arising from the measurement of the electron EDM and discuss by how much CP violation in the top-Yukawa coupling can contribute to the baryon asymmetry of the Universe.

The Feynman period of a graph is a complicated integral that contributes to the running of the coupling in quantum field theory. Non-isomorphic graphs can sometimes yield the same period, and such symmetries simplify calculations. I will discuss other graph invariants, that are easier to compute, but still share the same symmetries of the Feynman period. In particular, I will focus on two such invariants obtained from counting minimal 6-cuts and the Martin polynomial of a 4-regular graph. These new invariants yield improved numerical approximations of Feynman periods, and they also provide further support for conjectured new symmetries.

We consider Drell-Yan lepton pairs produced in hadronic collisions. We implement the transverse-momentum (qT) resummation up to next-to-next-to-next-to-leading logarithmic (N3LL) accuracy and the qT subtraction formalism up to next-to-next-to-next-to-leading order (N3LO). We propose a method to consistently remove the fixed-order linear power corrections in qT which appears when fiducial kinematical cuts are applied on the final state system. This method enable us to provide predictions for fiducial cross sections with numerical accuracy at the permille level. Our calculation has been implemented in the public numerical program DYTurbo, which produces fast and precise predictions with the full dependence on the final-state leptons kinematics. We present illustrative numerical results at LHC energies.

We review some results about SU(2)-representations of fundamental groups of 3-manifolds, and notably those obtained by instanton gauge theory, and its relevance to 3-manifold topology. We will then explain some key techniques in more detail, some of which are related to area-preserving geometry of the 2-torus.

We derive Yangian Ward identities for the infinite class of four-point ladder integrals and their Basso-Dixon generalisations. These symmetry equations follow from interpreting the respective Feynman integrals as correlation functions in the bi-scalar fishnet theory. The Ward identities take the form of inhomogeneous extensions of the partial differential equations defining the Appell hypergeometric functions. We employ a manifestly conformal tensor reduction in order to express these inhomogeneities in compact form, which are given by linear combinations of Basso-Dixon integrals with shifted dimensions and propagator powers. The Ward identities naturally generalise to a one-parameter family of D-dimensional integrals representing correlators in the generalised fishnet theory of Kazakov and Olivucci. When specified to two spacetime dimensions, the Yangian Ward identities decouple. Using separation of variables, we explicitly bootstrap the solution for the 2D box integral. The result is a single-valued linear combination of Yangian invariant products of Elliptic K functions.

In this talk we will consider the radiation of two or more soft partons in QCD hard-scattering at one-loop order. Using regularization in d = 4 - 2epsilon space-time dimensions, we will explicitly show the ultraviolet and infrared divergent (epsilon-pole) terms of the one-loop soft current for emission of an arbitrary number of soft partons in a generic hard-scattering process. Then we will consider the specific case of soft quark–antiquark (qqbar) emission and we will write the one-loop current by including the finite terms. We will show that the one-loop soft-qqbar current exhibits a new type of transverse-momentum singularity, which has a quantum (absorptive) origin and a purely non-abelian character. At the squared amplitude (cross section) level, this transverse-momentum singularity produces contributions to multijet production processes in hadron collisions. Finally we will discuss also the extension of these results to the cases of QED and mixed QCD×QED radiative corrections for soft fermion–antifermion emission.

Consider a smooth manifold with a Riemannian metric satisfying some sort of curvature constraints like, for example, positive scalar curvature, non-negative Ricci or negative sectional curvature, being Einstein, Kähler, Sasaki, etc. A natural question to study is then what the space of all such metrics does look like. Moreover, one can also pose this question for corresponding moduli spaces of metrics, i.e., quotients of the former by (suitable subgroups of) the diffeomorphism group of the manifold, acting by pulling back metrics. These spaces are customarily equipped with the topology of smooth convergence on compact subsets and the quotient topology, respectively, and their topological properties then provide the right means to measure 'how many' different metrics and geometries the given manifold actually does exhibit; but one can topologize and view those also in very different manners. In my talk, I will report on some general results and open questions about spaces and moduli spaces of metrics with a focus on non-negative Ricci or sectional curvature as well as other lower curvature bounds on closed and open manifolds, and, in particular, also discuss broader non-traditional approaches from metric geometry and analysis to these objects and topics.

The Muon g-2 experiment at Fermilab has recently confirmed Brookhaven's earlier measurement of the muon anomalous magnetic moment a_μ. This new result increases the discrepancy Δa_μ with the Standard Model (SM) prediction and strengthens its 'new physics' interpretation. On the other hand, a recent lattice QCD result weakens this discrepancy. In this talk I will review the SM prediction of the muon g-2, focusing on some of the latest developments, and discuss the connection of the discrepancy Δa_μ to precision electroweak predictions via their common dependence on hadronic vacuum polarization effects. I will also briefly present the recently proposed MUonE experiment at CERN, where fixed-target muon-electron scattering will provide a new direct determination of the leading hadronic contribution to the muon g-2.

It is well known that the Poincaré group is the symmetry group of special relativity. In general relativity, sensible symmetry groups exist only for special spacetimes: the so-called asymptotically flat spacetimes. In this setting, mass is (essentially) concentrated in a compact region and the metric tensor decays to the Minkowski metric when going to infinity. Several groups have been proposed as generalizations of the Poincaré group in this setting. The most famous ones are the Bondi-Metzner-Sachs (BMS) group and the Newman-Unti (NU) group. We will briefly recall these groups and their relevance. It turns out that the BMS and NU groups are infinite-dimensional groups. We will present our recent results which establish the infinite-dimensional Lie theory for these groups.

We propose a method to produce precise Monte Carlo estimates of multi-scale multi-loop integrals directly in Minkowski space. The validity of our strategy is corroborated by presenting several examples ranging from one to three loops. When used in connection with four-dimensional regularization techniques, our treatment can be extended to ultraviolet and infrared divergent integrals.

The early inspiral phase of compact binary systems can be described in a post-Newtonian expansion in small constituent velocities and weak gravitational interaction. Using nonrelativistic effective field theories and techniques for multiloop calculations developed in particle physics, we obtain the fifth-order conservative contribution in this expansion. We present results for a number of observables.

We present a benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. To identify such configurations, we exploit Grover's algorithm for querying multiple solutions over unstructured datasets, which presents a quadratic speed-up over classical algorithms when the number of solutions is much smaller than the number of possible configurations. A suitable modification is introduced to deal with topologies in which the number of causal states to be identified is nearly half of the total number of states. The output of the quantum algorithm in IBM Quantum and QUTE Testbed simulators is used to bootstrap the causal representation in the loop-tree duality of representative multiloop topologies. The algorithm may also find application and interest in graph theory to solve problems involving directed acyclic graphs.

I present recent calculations of the relation between the kinetic and on-shell mass and the semileptonic b -> c decay rate to O(alpha_s^3). Both quantities are important ingredients for the inclusive determination of |V_{cb}| from inclusive B decays. The calculation of the decay rate is performed in an asymptotic expansion around the limit m_c ~ m_b and shows large perturbative corrections in the on-shell scheme. However, by changing to the kinetic scheme for the bottom quark mass the convergence of the perturbative series can be greatly improved. Since the expansion shows decent convergence even for m_c -> 0 we can also extract third order corrections to b -> u and muon decays.

Quantum field theoretic techniques can be used to calculate classical gravitational scattering of black holes (or neutron stars) relevant for gravitational-wave observations. Two current frontiers are the inclusion of spin and finite-size effects. We introduce on-shell variables for Heavy Particle Effective Theories (HPETs) with the goal of extending Heavy Black Hole Effective Theory---the gravitational analog of Heavy Quark Effective Theory---to higher spins and facilitation its application to higher post-Minkowskian orders. These variables inherit the separation of spinless and spin-inclusive effects from the HPET fields, resulting in an explicit spin-multipole expansion of the three-point amplitude for any spin. For finite-size effects we apply the Hilbert series to classify and construct all tidal operators involving two powers of the curvature.

After a short introduction to the λ-model, I will discuss the construction of integrable deformations by employing an asymptotic limit on λ-deformations of non-compact coset CFTs. Specifically, I will focus on a 2D and a 3D example. After the asymptotic limit, the new models interpolate between a CFT with a linear dilaton and a hyperbolic space in two and three dimensions respectively. The existence of a new zoom-in limit in λ-deformed models will also be discussed.

In the talk we discuss the renormalization of the electric charge, as defined in the Thomson limit, with the aim to express the charge renormalization constant in terms of self-energies of the photon-Z-boson system in an arbitrary R_xi-gauge to all perturbative orders. The derivation as carried out in the Standard Model holds in all spontaneously broken gauge theories with the SU(2)_w * U(1)_Y gauge group in the electroweak sector and is based on the application of charge universality to a fake fermion with infinitesimal weak hypercharge and vanishing weak isospin, which effectively decouples from all other particles. Charge universality, for instance, follows from the known universal form of the charge renormalization constant as derived within the background-field formalism. Finally, we briefly discuss the generalization of the described procedure to gauge theories with gauge group U(1)_Y * G with any Lie group G, only assuming that electromagnetic gauge symmetry is unbroken and mixes with U(1)_Y transformations in a non-trivial way.

I will discuss when a supergravity solution, belonging to a consistent truncation on an internal sphere, is guaranteed to have some degree of separation in its Hamilton-Jacobi equation. This talk is based on https://arxiv.org/abs/2102.12493, where it is shown that such separability can be guaranteed if sufficient isometries along the internal sphere are preserved, in addition to an appropriate restriction of the reduction gauge vectors. A classification of such sufficient 'separable isometries' may be of practical use in the generation of separable solutions within a given consistent truncation, which are conveniently amenable to scalar probe calculations. On the other hand, our results suggest that a supergravity solution with a separable massless Hamilton-Jacobi equation may be a tell tale sign that it belongs to an underlying consistent truncation, providing a simple diagnostic in the search for new consistent truncations, as occurred in the motivating example of https://arxiv.org/abs/2004.13031​​.​

One of the major challenges in computing higher-order corrections of collider observables is the treatment of infrared singularities. Local Unitarity (LU) is a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its real-emission and virtual degrees of freedom. In this talk I will introduce the key concepts behind LU and will show how it can be used to produce differential cross sections with the push of a button.

Infrared problems in the evaluation of gauge-theory amplitudes and cross sections have been a focus of theoretical research for close to a century. Yet, new discoveries and new ideas continue to emerge, and high-precision phenomenology requires further sharpening of our tools. I will review our present understanding of the infrared structure of non-abelian scattering amplitudes, emphasising the ideas of universality, factorisation, evolution and resummation. I will briefly introduce new ideas for the analysis of soft divergences using conformal field theory tools, and finally I will discuss the problem of infrared subtraction for high-order predictions of complex collider observables.

The computation of master integrals is one of the key problems in modern precision high energy physics. In this talk, we would introduce the improved auxiliary mass flow method to numerically compute master integrals. This improved version has much better performance than the original one introduced several years ago in arXiv: 1711.09572, such that many cutting-edge problems are now computable in this framework. As examples, we calculate master integrals involved in two-loop electroweak correction to e+e- -> HZ, two-loop QCD corrections to 3j, W+2j, H+2j, ttbarH, 4j and three-loop QCD correction to ttbar production. Our tests show that the method might be the most powerful one among currently existing numerical methods.

In this talk, I review the definition and applications of EL∞-algebras given in arXiv:2106.00108. EL∞-algebras are generalizations of L∞-algebras comprising weak Lie ∞-algebras, and they have a number of applications within extended geometry. In particular, they clarify the higher symmetry structure of generalized tangent bundles and double/exceptional field theory. They also provide the algebraic origin for data needed in the definition of higher gauge theories such as the tensor hierarchy of gauged supergravity. This Lie ∞-algebraic perspective now provides a clear path towards finite gauge transformations and a global picture of these higher gauge theories.

On 7th April, the first results from the g-2 experiment at Fermilab were published and have attracted huge world-wide attention. In this talk, the Standard Model prediction of g-2 of the muon is reviewed, with emphasis on the determination of the hadronic contributions which are the limiting factor for its uncertainty. Recent developments, the current state of the discrepancy between experiment and theory as well as future prospects will be discussed.

In this talk I will present recent results on the complete two-loop corrections in massless QCD for the production of two photons and a jet. The full colour structure of the amplitude is taken into account. In particular, we analytically compute all two-loop helicity amplitudes for the quark-antiquark, quark-gluon, and antiquark-gluon channel, and check them with an independent calculation of the polarisation-summed interference with the tree amplitude.

I will review the GENEVA framework, that combines the NNLL resummation of large Sudakov logarithms at small values of the jet resolution variable with multiple NLO matrix-element corrections to larger values, to give a complete description at the next higher perturbative accuracy in the strong coupling constant at both small and large jet resolution scales. The resulting NNLO event generator matched to parton showers allowed us to obtain results for several color-singlet processes, displaying good agreement in comparison with LHC data. Possible extensions of the method towards more complicated final states will also be discussed.

Recent flavor data show a reinforced set of deviations from the Standard Model predictions, pointing to violations of lepton flavor universality. I will critically review these data and discuss their theoretical interpretation, including their possible connection to the hierarchical pattern of fermions masses and mixing angles. To this end, I will first interpret the data following an effective field theory approach and later discuss possible UV completions. Complementary constraints and implications for future measurements will be also discussed.

Zoom 645 6733 6962 , Password 607723

The AdS/CFT correspondence is a powerful tool for studying strongly coupled QFTs by performing computations in string theory and its low energy limit, supergravity. I will review Exceptional Field Theory, a formalism that unifies gravitational and flux degrees of freedom of supergravity, and thereby makes a large exceptional symmetry group manifest. This large symmetry group simplifies many complicated calculations in AdS backgrounds, such as constructing consistent truncations or computing the spectrum of linearised fluctuations around AdS vacua. I will show how this can be used to gain insights into dstrongly coupled QFTs. Finally, it time permits, I will discuss applications to non-supersymmetric AdS vacua.

Exactly solvable models and holography; Listening to the shape of string theory's extra dimensions; Atomic systems for timing and sensing applications

Proposed in 1954 by Gell-Mann, Goldberger, and Thirring, crossing symmetry postulates that particles are indistinguishable from anti-particles traveling back in time. Its elusive proof amounts to demonstrating that scattering matrices in different crossing channels are boundary values of the same analytic function, as a consequence of physical axioms such as causality, locality, or unitarity. In this talk we report on the progress in proving crossing symmetry on-shell within the framework of perturbative quantum field theory. We derive bounds on internal masses above which scattering amplitudes are crossing-symmetric to all loop orders. They are valid for four- and five-point processes, or to all multiplicity if one allows deformations of momenta into higher dimensions at intermediate steps. As usual we will have our informal coffee meeting before the talk to simulate a coffee corner discussion. The zoom room will already be open from 3:30pm on. Feel free to join any time before the talk. Passcode upon request.

W-algebras associated to simple Lie algebras are non-linear generalisations of the Virasoro algebra, from which certain CFTs can be defined. Using a formalism of Kontsevich and Soibelman and representation theory of W-algebras via free fields (when this exist), one can construct from them systems of PDEs whose solution is computed by a topological recursion. Such solutions carry information about 2d (worldsheet) geometry, and topological recursion mean this information is reached by induction on the Euler characteristic that resembles a cutting/pasting approach. They are sometimes expressible as integrals on the moduli space of complex curves or as topological string A-model amplitudes (for certain target spaces), and gives suitable definition of topological string B-model for certain type of complex 1d singularities. I will give an overview of these connections, and describe if time permits sketch a more recent link (ongoing work) to Nekrasov partition functions in 5d gauge theories (in which W-algebra are known to appear since Alday-Gaiotto-Tachikawa proposal). This is based on joint works with Andersen, Chekhov, Orantin, Bouchard, Chidambaram, Creutzig, Noshchenko, Kramer, Schüler.

High energy particle collisions are an ideal framework for accessing new information on matter constituents and forces of Nature. Advances in Theoretical Physics depend on our ability to describe the scattering processes among elementary particles at very high accuracy. Theoretical Physicists calculate scattering amplitudes, numbers that are related to the probabilities of different aftermath of particle scattering, which encode the chance that a given set of particles will turn into certain other particles after an impact. Feynman graphs are a convenient way to represent particle collisions. The mathematical methods required to describe scattering events which take place from the smallest to the largest scale of the Universe benefit from concepts borrowed from the rich research in mathematical disciplines, such as (differential and algebraic) Geometry, Topology and Number Theory. In this seminar, I elaborate on the diagrammatic approach to Fundamental Interactions via Scattering Amplitudes and Feynman integrals, and on their algebraic properties which have been recently understood to be ruled by Intersection Numbers: a novel connection between Physics and Mathematics.

We will discuss the deformation theory of nearly G2-manifolds. After defining nearly G2-manifolds, we will describe some identities for 2 and 3-forms on such manifolds. We willintroduce a Dirac type operator which will be used to completely describe the cohomology of nearly G2-manifolds. Along the way, we will give a different proof of a result of Alexandrov-Semmelman on the space of infinitesimal deformation of nearlyG2structures. Finally, wewill prove that the infinitesimal deformations of the homogeneous nearly G2-structure on the Aloff–Wallach space are obstructed to second order. The talk is based on a joint workwith Ragini Singhal (University of Waterloo).

We will start by discussing a flow of isometric G2-structures. We consider the negativegradient flow of the energy functional restricted to the class of G2-structures inducing agiven Riemannian metric. We will discuss various analytic aspects of the flow includingglobal and local derivative estimates, a compactness theorem and a monotonicity formulafor the solutions. After defining an entropy functional we will prove that low entropy initialdata lead to solutions that exist for all time and converge smoothly to a G2-structure with divergence free torsion. We will also discuss finite time singularities and the singular set ofthe solutions. Finally, we will discuss the isometric flow ”coupled with the Ricci flow of the underlying metric, which again is a flow of G2-structures (and is a specific example of a familyof flows of G2-structures which we have introduced), and discuss some of its properties. This is a based on two separate joint works with Panagiotis Gianniotis (University of Athens)and Spiro Karigiannis (University of Waterloo)

Composite Higgs models are Beyond the Standard Model approaches involving a strongly coupled sector in which the Higgs particle is a Goldstone boson of a spontaneously broken symmetry, in analogy to pions in QCD. I will discuss gauge/gravity dual descriptions of explicit realizations of composite Higgs models using insights from non-conformal examples of the AdS/CFT correspondence. I will explain how to calculate particle masses and decay constants for proposed Sp(4) and SU(4) gauge theories. The results obtained compare favourably to lattice gauge theory studies and go beyond those due to a greater flexibility in choosing the fermion content. That content changes the running of the couplings and its choice can lead to sizable changes in the bound state masses. The `top partners’ present in composite Higgs are modelled by dual fermionic fields in the bulk. Including suitable higher dimension operators can ensure a top mass consistent with the Standard Model.

The anomalous magnetic moment of the muon serves as a low-energy precision test of the Standard Model of particle physics. The White Paper (arXiv:2006.04822) recently published in Physics Reports concludes that a tension of 3.7 standard deviations persists between the direct measurement and the Standard Model prediction of the anomalous magnetic moment of the muon. A new direct measurement is expected very soon by the E989 experiment at Fermilab. On the theory side, the uncertainty of the SM prediction is quasi-saturated by the hadronic contributions. I will focus on the effort by the lattice QCD community to compute these hadronic contributions and compare these calculations to phenomenological determinations.

With Run II, the LHC experiment already reached an unprecedented level of precision compared to previous hadron colliders. The amount of data collected in Run III and the High-Luminosity run will increase quickly and dramatically. I will discuss specific challenges to theorists that must be overcome to provide predictions that have the precision necessary to match the accuracy of data. A few novel ideas to exploit this precision directly or indirectly will also be discussed.

The nascent field of gravitational wave (GW) science will be an interdisciplinary subject — enriching different branches of physics — yet the associated computational challenges are enormous. Faithful theoretical templates are a compulsory ingredient for data analysis and reliable physical interpretation of the signals. Yet, while current templates for compact binary sources may be sufficient for detection and crude parameter estimation, they are still too coarse for precision physics with GW data. We then find ourselves in a situation in which, for key processes within empirical reach, theoretical uncertainties may dominate. To move forward, and profit the most from GW observations, more accurate waveforms will be needed. This will be critical, as I will discuss, to study the equation of state of neutron stars and the nature of black holes; as well as potentially successful searches for exotic compact objects and putative ultra-light (dark matter) particles in the Universe. The ‘effective field theory approach’ to the binary inspiral problem in general relativity — which my collaborators and I have developed — has been instrumental for the construction of the state-of-the-art GW template bank. I will review how these and other novel techniques borrowed from particle physics have transformed the study of the two-body problem in gravity, providing key new results and paving the road forward to a new era of foundational investigations in physics through GW precision data.

In the talk, the energy-momentum (also "stress-energy") tensor will be presented as crucial current density for the gravitational field. With its property of being conserved it necessarily generates a massless spin-2 gauge field which, by considering gauge and coordinate transformations becomes part of the spacetime metric. Beyond, the energy-momentum tensor is delivering deep insight into gravitation in thermodynamics, particularly interrelations between heat current, viscosity, temperature, entropy and entropy production under themselves and with respect to gravity will be discussed.

QED radiative corrections to hadronic observables are generally rather small but they become phenomenologically relevant when the target precision is at the percent level. This is the case of leptonic and semileptonic decays of light and heavy pseudoscalar mesons. On the one hand, QED radiative corrections to hadronic observables can be calculated with the required non-perturbative accuracy by using lattice techniques. On the other hand, the inclusion of electromagnetic interactions in a lattice calculation is a challenging problem because QED is a long-range unconfined interaction and numerical simulations necessarily require a finite volume. The problem is particularly delicate in the case of QED radiative corrections to decay rates because of the appearance of infrared divergences (proportional to the logarithm of the lattice volume) at intermediate stages of the calculations. In this talk I will briefly review the recent theoretical advances that opened the way to realistic non-perturbative simulations of QCD+QED, discuss a method that allows to calculate QED radiative corrections to hadronic decay rates and present the results of a non-perturbative calculation of the leptonic decay rates P-> l nu (gamma) in the case of light (P=pi,K) and charmed (P=D,Ds) pseudoscalar mesons.

The status of string theory will be examined, and what is known and what is unknown about the theory will be discussed. String theory has special duality symmetries that do not occur in conventional field theories, and some of the implications of these will be explored, and the implications for the nature of space-time will be investigated.

Weak capture transfer occurs when a particle becomes captured into orbit about one of the primary mass points of the three or four-body problem, temporarily. Capture in this case is defined when the Kepler two-body energy of a particle with respect to the primary is negative. This was first numerically demonstrated by Belbruno (EB) in 1986. This capture occurs in a region about the primary called a weak stability boundary (WSB). It was proven by EB (2005) that the WSB contains within it a hyperbolic invariant set, giving rise to chaotic motion. Although crudely numerically estimated in 1986, numerical work by Gomez (2007) gave deeper insights into its makeup yielding surprising results as to its complexity. Further insights in the makeup of this region were made in a series of studies (Gidea,Topputo, EB). The relationship of weak capture to permanent capture and the work of Sitnikov in the 1960s is discussed. Weak capture transfer has important applications. One such transfer was used in 1991 by EB and Miller to rescue an errand Japanese lunar probe and successfully send it to the Moon. This same transfer class was used in 2011 for NASA’s lunar Grail mission and another type was used by ESAs lunar SMART 1 mission in 2004. One such transfer is currently being used in a mission to Mercury for ESA’s BepiColombo mission. A new result that is described is the existence of a weak capture transfer to Mars. This promises to have interesting applications. A lunar gateway is also discussed based on recent work. If there is time, an exciting new application of weak capture to quantum mechanics is discussed.

Gravitational wave observations provide a new and unique window into the early universe. I will start by explaining why this is the case, and give an overview of new physics scenarios that give rise to a stochastic gravitational wave background in the early universe, and therefore may be testable by future gravitational wave observations. Then I will focus on the audible axion scenario, a class of axion models whose cosmological evolution leaves an observable imprint in the gravitational wave background. This allows a new and unique probe of very high scale axions, with symmetry breaking scales close to the GUT or string scale.

The Swampland program aims to distinguish effective field theories that can be consistently completed into quantum gravity in the ultraviolet from those which cannot. It has lead to a number of proposals, or conjectures, regarding the required properties of effective theories. I will review some of the evidence for these and propose that they arise due to a particular aspect of duality where propagating fields in the infrared are emergent from the collective properties of infinite towers of states. Time permitting, I will discuss some applications of the conjectures, in particular to accelerating cosmologies and to massive spin-2 fields.

Dyson-Schwinger equations are the quantum analogues of the equations of motion and so are physically very important and useful. In their diagrammatic form they also show some nice discrete mathematical structures. For example, diagrammatically they generate certain classes of Feynman diagrams and so act like combinatorial specifications, and they are compatible with algebraic structures on Feynman diagrams, like renormalization Hopf algebras. In this colloquium I will overview the physics and the math of this and close with a different combinatorial expansion that can go beyond naive Feynman diagrammatics and solve some Dyson-Schwinger equations using an unusual expansion indexed by rooted connected chord diagrams.

In the planar limit of a large number of colors, N=4 super Yang-Mills theory is integrable, and remarkable advances have been made in determining operator anomalous dimensions and more to all loop orders. In this talk I'll describe recent progress in constructing scattering amplitudes in this theory to high loop order. Planar N=4 amplitudes are dual to light-like polygonal Wilson-loops, and are only nontrivial for six or more gluons. The spaces of functions to which the amplitudes belong are so restrictive that only a few constraints are needed to simply write down the answer, through seven loops in the six-gluon case and four loops in the seven-gluon case. The results are multi-variate functions of the kinematics, which can be analyzed in various limits in order to study how high loop order amplitudes factorize. One can also extrapolate from weak to strong coupling, and compare with the AdS/CFT dual description available there.

This talk is about integrability of planar N=4 super Yang-Mills theory. I will review the notion of integrability in the AdS/CFT context and what it means for planar scattering and Wilson loops including selected results. I will then present a concrete notion of the corresponding Yangian symmetry in this model, show that it holds true, and discuss the (perturbative) implications for correlation functions and Wilson loops.