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.

The hexagon formalism provides a framework to calculate correlation functions in N=4 Super Yang-Mills theory using integrability. The basic idea is to decompose the correlation function into building blocks called hexagon form factors. These hexagon patches can be glued back together by dressing their non physical edges with virtual magnons and integrating over their respective rapidities. The approach will be demonstrated on the example of the one-loop correction to a correlation function of five BPS Operators of length two. Here it is necessary to glue three adjacent hexagon patches, which involves the scattering of two virtual magnons. We will calculate parts of this process analytically using a simplified form of the corresponding scattering matrix.

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.

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.

We first give a brief status of the field of multi-loop calculations, with focus on integrals with many mass scales and phenomenological applications. Then we discuss representations of loop integrals in Feynman parameter space and their evaluation with sector decomposition methods.This will lead us to asymptotic expansions of integrals, for example in the small mass limit or the high energy limit, also known as “expansion by regions”. We will discuss a geometric formulation of such expansions in integration parameter space and present the automation of such expansions within the program pySecDec.

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.

After a short but gentle recap of noncommutative geometry we show that the spectral action, when perturbed by a gauge potential, can be written as a series of Chern-Simons actions and Yang-Mills actions of all orders. In the odd orders, generalized Chern--Simons forms are integrated against an odd $(b,B)$-cocycle, whereas, in the even orders, powers of the curvature are integrated against (b,B)-cocycles that are Hochschild cocycles as well. In both cases, the Hochschild cochains are derived from the Taylor series expansion of the spectral action tr(f(D+V)) in powers of V=pi_D(A), but unlike the Taylor expansion we expand in increasing order of the forms in A. As a consequence of our expansion and of the gauge invariance of the spectral action, we show that the odd (b,B)-cocycle pairs trivially with K_1.

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.

The renormalization of the supersymmetric Wess-Zumino model is carried out to five loops in both the MSbar and momentum subtraction schemes. The model is the supersymmetric extension of scalar phi^3 theory but is renormalizable in four rather than six dimensions. The calculation is carried out in superspace meaning the D-algebra can be implemented automatically paving the way for the Mincer and Forcer packages to be employed to compute the Feynman integrals. Endowing the basic chirally symmetric theory with an O(N) symmetry means the five loop result can be checked against the known large N exponents. We also consider a generalization of the model with a tensor coupling similar to that used for percolation problems in non-supersymmetric phi^3 theory. In this case we reproduce the five loop part of Bellon and Schaposnik's 2008 construction of the Hopf algebra Schwinger-Dyson solution of the beta-function.

I will outline how (exceptional) generalised geometry secretly governs the physics of probe branes. Currents on the worldvolume naturally organise in the same multiplets appearing in the tensor hierarchy, and their current algebra takes a universal geometric form. The technical tool for this is an AKSZ-like construction of a Poisson algebra --- the brane phase space --- from the data of a QP manifold; i.e. from the L_infinity-algebra structure of gauge transformations of the (super)gravity background. This talk will be based on https://arxiv.org/abs/2103.08608

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.

In the theory of renormalisation of quantum field theories (a la Connes and Kreimer), character groups of certain Hopf algebras appear as “renormalization groups”. Here the Hopf algebra encodes the combinatorics underlying renormalisation, while the group hosts objects and equations of interest (such as time ordered exponentials and objects related to the Birkhoff factorization). The aim of this talk is to discuss the infinite-dimensional Lie group structure of the renormalization groups. Note that these groups are not naturally modelled on Banach spaces, so we will start with an introduction to what we actually mean by “infinite-dimensional Lie group”. No prior knowledge will be assumed as we review the basic concepts (calculus beyond Banach spaces, infinite dimensional Lie groups) and discuss some key properties of these infinite-dimensional groups.

I will discuss recent progress towards understanding geometric and holographic aspects of electromagnetic duality in four-dimensional supergravity. More concretely, I will focus on the connection between electromagnetic duality and the existence of new classes of S-fold backgrounds of type IIB supergravity of the form AdS4 x S1 x S5 which are conjectured to correspond to new strongly coupled three-dimensional CFT’s on a localised interface of SYM. I will discuss holographic RG flows on the D3-brane that generically connect anisotropic deformations of SYM in the UV to various S-fold CFT’s in the IR with different amounts of supersymmetry and flavour symmetries. Lastly, a geometric interpretation of axionic deformations will be provided in terms of monodromies on the internal S5 when moving around the S1.

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.

n recent years much progress has been made in the field of non-relativistic physics. In particular, in this talk I will focus on the journey going from non-relativistic particles to strings and finally to membranes. I will discuss how these theories can be obtained in different ways, e.g. via limiting procedures or via embedding in the more general frameworks of Double Field Theory (DFT) and Exceptional Field Theory (ExFT). These provide tools that are especially useful for understanding the symmetries and degrees of freedom of the theories. An example is given by the scalar Poisson equation which, as we will see, cannot be obtained by variation of an action. DFT/ExFT explain naturally how and why this equation cannot be derived from an action principle.

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

After a short review of some salient features of E7 and E8 exceptional field theories, I will formulate their E11 generalisation. This exceptional field theory for the Kac-Moody group E11 combines consistently ideas of Peter West, Olaf Hohm, Henning Samtleben and many others. I will explain in particular how one recovers the eleven-dimensional supergravity Lagrangian, together with an infinity of non-linear duality equations for higher rank tensors including the dual graviton. This is a work in collaboration with Axel Kleinschmidt and Ergin Sezgin.

I report on work in progress with Ömer Gürdoğan, Erik Panzer and Matteo Parisi on the analytic structure of Feynman integrals in the parametric representation. More generally, we consider integrals of (relative) meromorphic differential forms over relative cycles, both living in the complement of a subspace arrangement in a compact complex manifold. If the form and/or the cycle depend on additional parameters (e.g. masses, momenta in the Feynman case), such integrals define complex-valued functions on the space of parameters. Our goal is to study the singularities (branch points, discontinuities) of these functions using the classical framework developed by Pham et al. (based on the work of Landau, Leray, Thom, Picard, Lefschetz etc.). In the relative case, however, the necessary tools are at most implicitly contained in the existing literature, if at all. I will describe how to fill this gap, i.e. our proposed setup for a 'relative Picard-Lefschetz theory', and show how a careful analysis of the involved geometry and topology leads to a nice conjecture on the iterated structure of the singularities of such functions, generalising the symbol calculus in the case of polylogarithms.

Upon dimensional reduction to two spacetime dimensions, (super)gravity exhibits an infinite-dimensional duality symmetry based on an affine Lie algebra. I will review the construction of the associated exceptional field theory which, in the maximally supersymmetric case, provides a (formally) E9-covariant reformulation of eleven-dimensional and type IIB supergravity. I will present two equivalent descriptions of its dynamics, which both rely on a pseudo-Lagrangian supplemented by a twisted self-duality equation, and highlight features which do not appear in other exceptional field theories.

Generalizing the point-like interactions of standard ``local'' QFT to combinatorially non-local interactions preserves locality in the sense of renormalization. The crucial difference is that residues come with an additional graph structure. Still, the standard Hopf-algebraic structure of (perturbative) renormalization applies. I show how this facilitates renormalization in the case of the BPHZ momentum scheme and give an outlook on non-perturbative applications.

I will review recent breakthroughs in understanding on-shell heterotic moduli from the past decade, many of which required thinking in terms of generalised geometry, doubled field theory and L-infinity algebras. In most of these formulations an extra set of End(TX)-valued are needed for the description to make sense. These unphysical fields are often given the interpretation of field redefinitions. I will take some modest steps towards an understanding of the moduli problem without these spurious degrees of freedom. In particular, I will describe the cohomology which counts the infinitesimal massless modes.

I will discuss phenomenological consequences of merging the proper QCD Sudakov resummation with small-x effects, which allows one to compute gluon distributions that depend on longitudinal momentum, transverse momentum and the hard scale of the process. The small-x resummation is included by means of the Balitsky-Kovchegov equation supplemented with a kinematic constraint and subleading corrections. The new gluon densities are then used to calculate predictions for central-forward dijet production at LHC within the framework of high energy factorization. The results are tested against CMS data and compared with earlier predictions, where Sudakov effects were coming from naive modeling.

I will review recent progress on the perturbative renormalization of quantum gravity: Following a suggestion of Kreimer (2007) and results of van Suijlekom (2007), we study the relationship between gravitational Slavnov--Taylor identities and Hopf ideals [DP, 2019]. This includes some combinatorics with the superficial degree of divergence and the extension of coproduct identities to the non-renormalizable case. We proceed by displaying gravitational Feynman rules for arbitrary vertex valence and for a one-parameter quadratic de Donder gauge fixing [DP, 2020]. In particular, we study the longitudinal and transversal properties of the gravitational Feynman rules using the respective projection tensors [DP, in prep.]. Specifically, we comment on the relationship between the two commonly used metric decompositions, the deviation of the flat background metric and the inverse metric density decomposition. This leads us to define an intermediate metric decomposition, whose transversal structure is symmetric and thus similar to the situation in Quantum Yang--Mills Theory. We close with a comment on the respective Feynman graph cohomology, as defined by Kreimer et al. (2013) in the context of Quantum Yang--Mills Theory.

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.

I will report on recent progress with Bouchard, Chidambaram and Creutzig establishing that Whittaker vectors (also called Gaiotto vectors and representing instanton partition function on equivariant C^2) and the Nekrasov partition function (of instantons on equivariant P^2) for N = 2 supersymmetric gauge theory with gauge group SU(n) can be computed by the topological recursion. The starting point is a form of the Alday-Gaiotto-Tachikawa conjecture established by Schiffman-Vasserot and Braverman-Nakajima-Finkelberg and stating that the cohomology of a suitable compactification of the moduli space of G-bundles on P^2 carries an action of the W(gl_r) algebra and the fundamental class is a Whittaker vector for this action. Our approach suggests a route to prove rigorously that the all-order hbar = -epsilon_1 epsilon_2 expansion of the Whittaker vector partition function can be extracted (by means of the topological recursion) from the Seiberg-Witten curve.

I will start by giving a short introduction to the higher spin gravity, overviewing very briefly a history of the subject and the most important results, including no-go theorems, Vasiliev equations, Klebanov-Polyakov conjecture etc. Then I plan to discuss in some more details the Vasiliev theory that provides a consistent model of interacting massless higher-spin fields in AdS space. Finally, I will review a recent progress in the field, in particular regarding the issue of locality of higher spin interactions, and will discuss some topics for the future research, related to the off-shell completion and quantization of Vasiliev theory. ### Meeting id: 942 2450 6869 Password: 009633

The interest in the analytical structure of Feynman integrals dates back to the 1950s and Landau's famous approach. And due to various methods based on "unitarity cuts", interest in the singularities of Feynman integrals has unabated to this day. However, many heuristically motivated statements from this time have still lacked a solid mathematical basis. This is not least due to the fact that many of the necessary mathematical methods were only developed later. Recently, more efforts have been made to compensate for this lack of mathematical foundation. In this talk, we will consider the singularities of the Feynman integral from the perspective of Gelfand-Kapranov-Zelevinsky (GKZ) hypergeometric systems and describe them as A-discriminants. The advantage of this approach is that we can draw on a large arsenal of already known properties of this GKZ theory. After a short introduction to the methods of GKZ, we will present a few of these properties.

Chiral fermions have the property that their left-handed and right-handed components transform differently under some symmetry. Folklore suggests that it is impossible to give such fermions a mass without breaking this symmetry. I'll show, through a number of examples, why this folklore is wrong. In particular, I'll show how one generation of fermions in the Standard Model can get a mass without the need for a Higgs boson that breaks electroweak symmetry. ### Meeting id: 942 2450 6869 Password: 009633

In the talk I will describe the concept of G-algebroid, which generalises both Lie and Courant algebroids, as well as the Leibniz algebroids used in the description of exceptional generalised geometry (at least for n<7). I will discuss a classification result in the "M-theoretic exact" case and then employ G-algebroids to define and study a general concept of "Poisson-Lie duality", recovering in particular the recently introduced Poisson-Lie U-duality. This is a joint work with Mark Bugden, Ondrej Hulik, and Daniel Waldram.

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.

Drell-Yan production of a charged lepton pair is a key process at the Large Hadron Collider. The region of large invariant mass region is of particular interest for new physics searches, which motivates precise theory predictions at energies well above the Z resonance. In this talk, I discuss our recent calculation of the mixed electroweak-QCD two-loop amplitudes for the process qq->l+l- as a further step in this direction. I present the calculation in two different approaches, the ’t Hooft-Veltman-Breitenlohner-Maison (HVBM) gamma5 scheme and Kreimer's anticommuting gamma5 scheme, and discuss how one arrives at scheme-independent results. In the HVBM scheme, we restored chiral symmetry using local counter terms, where we found it essential to consistently calculate them to higher orders in (d-4).

At the J-PARC KOTO experiment, we are searching for a rare decay, KL -> pi0 nu nu-bar, to study new physics beyond the Standard Model. With the data taken from 2016 to 2018, we recently set an upper limit of 4.9E-9 (90% CL) on the branching ratio of the decay, based on 3 observed events and 1.22 +- 0.26 background events. At the KAON2019 Conference, we showed 4 events in the signal box because that is what we observed when we opened the box. Since we did not understand the origin of those events, we simply reported the facts, and did not present any physics results. However, many theorists called it “KOTO anomaly”. By studying further, we later discovered two new background sources. This talk presents experimental explanation of the KOTO anomaly

The canonical approach for tackling higher-order computations involves splitting up a finite quantity into two separately divergent ones. First, multiloop amplitudes are evaluated using (mostly) analytical techniques. Second, phase-space integrals are computed using numerical Monte-Carlo techniques with ad-hoc subtraction terms for regularising soft and/or collinear infrared divergences. We will present our recent work, Local Unitarity, in which we propose a radically different technique whereby the singularities in real-emission and virtual degrees of freedom directly cancel without the use of any counterterms and at any perturbative order. On the practical side, this allows for the fully numerical computation of differential corrections, potentially alleviating the complexity bottleneck analytical alternatives are facing. From a theoretical standpoint, our proof of the local cancellation of infrared singularities sheds new light on the exact mechanism by which it is realised.

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.

With null results in resonance searches at the LHC, the physics potential focus is now shifting towards the interpretation of non-resonant phenomena. An example of such shift is the increased popularity of the EFT programme. We can embark on such programme owing to good integrated luminosity and an excellent understanding of the detectors, which will allow these searches to become more intense as the LHC continues. In this talk I will explain a framework to perform this interpretation in terms of a diverse set of scenarios, including 1.) generic heavy new physics described at low energies in terms of a derivative expansion, such as in the EFT approach, 2.) very light particles with derivative couplings, such as axions or other light pseudo-Goldstone bosons, and 3.) the effect of a quasi-continuum of resonances, which can come from a number of strongly-coupled theories, extra-dimensional models, clockwork set-ups and their deconstructed cousins.

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).

I will discuss the factorisation and the subtraction of infrared singularities for scattering amplitudes and cross sections relevant for collider phenomenology. In particular, I will focus on the relation between the factorisation of soft and collinear poles in fixed-angle scattering amplitudes and the construction of local counterterms for singular contributions to real radiation. This approach leads to general definitions of soft and collinear counterterms to all orders in perturbation theory, and suggests promising simplifications for the construction of subtraction algorithms beyond NLO.

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)

Over the next years, measurements at the LHC and the HL-LHC will provide us with a wealth of data. The best hope of answering fundamental questions like the nature of dark matter, is to adopt big data techniques in analyses and simulations to extract all relevant information. At the analysis level, machine learning methods have already shown impressive performance boosts in many areas like top tagging, jet calibration or particle identification. On the theory side, LHC physics crucially relies on our ability to simulate events efficiently from first principles. In the coming LHC runs, these simulations will face unprecedented precision requirements to match the experimental accuracy. Innovative ML techniques like generative models can help us overcome limitations from the high dimensionality of the parameter space. Such networks can be employed within established simulation tools or as part of a new framework. Since neural networks can be inverted, they also open new avenues in LHC analyses.

Efficient numerical algorithms for the construction of one-loop amplitudes have played a crucial role in the automation of NLO calculations, and similar algorithms at two-loop level are highly desirable in order to achieve the precision of theoretical predictions required for the LHC. Numerical tools construct the numerator of loop integrals in four dimensions, while the missing contributions stemming from the interplay of (D-4)-dimensional numerator parts with 1/(D-4) poles have to be reconstructed separately. At one-loop level a well-established method is to restore these contributions through process-independent rational counterterms. In this talk we extend the concept of rational terms of UV origin to two loops. We present a master formula for the computation of D-dimensional two-loop scattering amplitudes from amplitudes with four-dimensional numerators and a finite set of universal rational counterterms. A generic method to compute such rational terms from simple tadpole integrals will be discussed, as well as the renormalisation scheme dependence of rational terms. Finally, we present the complete set of two-loop rational terms in SU(N) and U(1) gauge theories in a generic renormalisation scheme.

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.

In this talk, we outline the computational details and present the results for NNLO mixed EWxQCD corrections to on-shell production of Z boson at the LHC. We use the method of differential equation to obtain all the master integrals analytically, appearing in virtual and real-emission contributions. These results increase the accuracy of the predictions and contribute to reduce the theoretical uncertainties.

Using the Gelfand-Kapranov-Zelevinsk system for the primitive cohomology of an infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop order minus one, we completely clarify the analytic structure of all banana amplitudes with arbitrary masses. In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds to the point of maximal unipotent monodromy, is determined by a novel Γˆ-class evaluation in the ambient spaces of the mirror, while the imaginary part of the amplitude in this regime is determined by the Γˆ-class of the mirror Calabi-Yau manifold itself. We provide simple closed all loop formulas for the former as well as for the Frobenius κ-constants, which determine the behaviour of the amplitudes, when the momentum square equals the sum of the masses squared, in terms of zeta values. We extend our previous work from three to four loops by providing for the latter case a complete set of (inhomogenous) Picard-Fuchs differential equations for arbitrary masses. This allows to evaluate the amplitude as well as other master integrals with raised powers of the propagators in very short time to very high numerical precision for all values of the physical parameters. Using a recent p-adic analysis of the periods we determine the value of the maximal cut equal mass four-loop amplitude at the attractor points in terms of periods of modular weight two and four Hecke eigenforms and the quasiperiods of their meromorphic cousins.

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.

Particle physics processes are usually modeled with a chain of complex simulators. While these allow us to generate high-quality simulated data, they face a challenging inverse problem when we want to infer theory parameters from observed data because the relevant likelihood function cannot be evaluated. I will explain this problem, review what the field has traditionally done to circumvent it, and show how we can use machine learning methods together with matrix-element information to solve it efficiently. Finally I will discuss how the same methods can be useful in many other scientific fields from neuroscience to strong gravitational lensing.

Calculation of virtual scattering amplitudes involves dealing with several problems. The presence of numerical instabilities, as well as singularities, prevents straightforwardly obtaining precise results. And most of these problems are due to the particular structure of the integrand-level expressions. By using the Loop-Tree Duality (LTD) formalism, and exploring the novel nested residue strategy, we recently managed to obtain causal representations of multi-loop amplitudes and classify diagrams according to their topological complexity. We did some numerical simulations, and verified the stability of the calculations. Besides that, in this talk we will focus on the potential consequences of these discoveries.

With the growing need for multi-loop multi-scale scattering amplitudes several approaches have been developed which aim at a more automated numerical computation of them. An example is the multi-loop numerical unitarity method with which we have computed the planar two-loop five-parton amplitudes in QCD, as well as the two-loop four-graviton amplitudes in Einstein gravity. In this talk we review those results and introduce the Caravel framework, a C++ library implementing algorithms required for numerical unitarity which we will make publicly available.

In this talk, I will discuss the analytical calculation of cusp and collinear anomalous dimensions in four-loop QCD. Our approach is based on a direct calculation of four-loop quark and gluon form factors. I will explain how finite field and novel syzygy techniques facilitated the reduction of the relevant Feynman integrals to a basis of finite integrals, which could then be evaluated directly from their standard parametric representation.

The stringent bounds on the electric dipole moment (EDM) of the electron provide a powerful test of new physics. They can probe new dynamics at the TeV scale, even when contributions to the electron EDM arise at the two-loop level. I will discuss how to use the effective-field-theory (EFT) approach to classify these corrections, presenting the contributions to the anomalous dimension of the CP-violating dipole operator of the electron up to the two-loop level. Selection rules based on helicity and CP symmetry play an important role in simplifying the analysis. I will also show that the latest ACME bound pushes natural theories significantly more into fine-tune territory, unless they have a way to accidentally preserve CP.

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 treatment of γ 5 in dimensional regularization has been an issue ever since the original ‘t Hooft-Veltman paper. By dropping cyclicity of traces involving γ 5, one can treat the d-dimensional γ5 as in four dimensions, at the cost of rendering certain Feynman integrals ambiguous. This ambiguity has been made manifest in the β4αS calculations of Bednyakov & Pikelner and Zoller, where the strong coupling, top Yukawa coupling and Higgs self-coupling have been taken into account, hence the ambiguity now has phenomenological consequences. In this talk, I will demonstrate how Weyl Consistency Conditions fix this particular ambiguity for a completely general theory, in a way that generalizes to higher orders. As an added bonus, given the 3-loop gauge β-function for a simple gauge group, I will indicate how the same method easily extends this result to the general case, including kinetic mixing.

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 this talk, I will discuss a framework to compute two-loop amplitudes that combines integrand reduction, integration-by-part identities, numerical evaluation over finite fields and analytic reconstruction techniques. Applications to the computation of planar two-loop five-parton and w+4 parton amplitudes in QCD will also be presented.

I will give a review of the status of Standard Model effective field theory (SMEFT) in the EW sector. The talk will showcasing some results from latest global fits, the state of the art in Monte Carlo tools and discuss some recent sensitivity studies from new processes at the LHC and beyond. The latter will focus first on the high energy behaviour of scattering amplitudes involving top quarks/ EW bosons and their embedding into collider processes as a new avenue for improving our understanding of the interactions of the electroweak symmetry breaking sector. Finally I will present a study of the ttbb final state as a probe of new four-fermion interactions between third generation fermions exploiting some multi-dimensional machine learning classifiers to optimise sensitivity.

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.

This seminar talk is intended as an interactive session about machine learning (ML) techniques and their use cases for particle physics. No prior knowledge about machine learning is required. Depending on the feedback of the audience, we may briefly go through some basic building blocks of more advanced ML models. The benefit of ML for the particle physics community will be illustrated with several examples including cross section regression, learning an exclusion boundary, event generation and anomaly detection. With my presentation I want to stimulate discussions about issues and doubts as well as potentials and ideals regarding the incorporation of ML methods into the physics workflow and am happy to discuss whatever use-case you have been dreaming of.

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.

In this talk, we describe a novel framework to obtain higher-order corrections to physical observables in perturbative QFT. This method, called Four-Dimensional Unsubtraction (FDU), is based on the Loop-Tree Duality (LTD) theorem, which provides an alternative decomposition of virtual amplitudes. The strategy is valid to all loop orders, even if multiple powers of the propagators are present. Through the introduction of fully local counter-terms, we manage to cancel the UV singular behavior. Moreover, the whole framework is intended to perform an integrand level combination of the real and virtual contributions, using properly defined universal kinematical mappings, to achieve a complete point-by-point cancellation of IR divergences. The final result can be directly integrated in four space-time dimensions, applying standard numerical techniques. Some examples for NLO corrections and two-loop amplitudes will be discussed.

Proposed future electron-positron colliders would allow precise determinations of the mass of the top quark and the W boson from measuring the rise of the cross section near the pair-production threshold. At hadron colliders, the threshold region is not directly accessible but enhanced by rising parton luminosities. Near threshold, radiative corrections due to soft and Coulomb photons or gluons are enhanced and can be resummed to all orders in perturbation theory. The cross section is also sensitive to the finite decay width of the produced particles. I will discuss an effective-field theory framework to address these effects and present recent results for top-quark pair production at the LHC and W-pair production at future lepton colliders.

After the discovery of the Top quark, high energy physics community took 17 years to find the Higgs boson in 2012. Since then, all Standard Model predicted fundamental particles are confirmed in experiments. In the next 15 years, the Large Hadron Collider (LHC) will focus on precision measurements of the Higgs boson properties. The precise theory predictions as well as the measurements of Higgs boson transverse momentum distributions, decay width and trilinear couplings will be crucial for searching beyond Standard Model singles, determining the stability of our universe and inspiring the next generation colliders. In this seminar, I will first summarise the state-of-the-art theory precisions of each Higgs boson production channels at the LHC. Then I will analyse the challenges and opportunities for precision Higgs phenomenology in the next 15 years till the end of High-Luminosity-LHC period.

Novel lattice results reveal a tension between the measured direct CP violation in K→εε decays and the standard model theory prediction, with the theoretical uncertainty dominating. This inconsistency could have several sources, one of which could be the missing contribution of new particles in the theory predictions. However, a reliable standard model prediction is needed to disentangle possible new physics effects from the standard model background. As rapid progress on the lattice is bringing non-perturbative long-distance effects under control, a more precise knowledge of short-distance contributions is essential. We describe the first NNLO calculation for this observable and discuss future prospects, as well as issues of scheme dependence and the separation of perturbative and non-perturbative effects.

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.

When solving functional equations, we tend to look first for an explicit representation of the solution, i.e., for an expression built from the indepen- dent variable and some constants by means of various basic operations. In this talk we will consider the problem of finding explicit solutions of homogeneous linear recurrence equations with polynomial coefficients (LRE). Algorithms are known for finding polynomial solutions, rational solu- tions, hypergeometric solutions (whose consecutive-term ratio is rational), d’Alembertian solutions (representable as nested indefinite sums of hypergeometric sequences) and Liouvillian solutions (representable as interlacings of d’Alembertian sequences) of LRE. Alas, usually no such solutions exist (save for the zero solution). So it is natural to think of wider classes of explicitly representable sequences, properly including Liouvillian sequences. Such classes can be obtained by allowing basic operations under which the class of Liouvillian sequences is not closed. One important operation of this kind is convolution of sequences which corresponds to the product of their generating functions. A convolution has the form of a definite sum, so the question arises: How to find solutions of LRE represented as (nested) definite sums of simpler sequences? #We will make a very small first step towards answering this seemingly difficult question.

One of the corner stones of future lepton colliders are high precision measurements of the top quark mass and width. In the first part of this talk, I present a new method for top quark mass determination at lepton colliders using radiative events, which can determine the top quark mass with an accuracy of 110 MeV. It relies on the inclusive top quark pair production cross section, which is known to high accuracy at the production threshold (NNLL and NNNLO) and at higher center-of-mass energies in the continuum (NNNLO QCD). For our study on radiative events, we have constructed a matched cross section, which I present in the second part of this talk. It is valid in all regions from the threshold to the continuum and combines NNLL threshold with NNNLO continuum contributions.

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.

Compact binaries composed of neutron stars and black holes are the most important source of grav-itational waves. The first observations of gravita-tional waves from binary black holes in 2015 was a landmark discovery for astrophysics and funda-mental physics. The detection of these waves and the extraction of the source’s parameters relies on accurate predictions for the gravitational waves. A combination of numerical and approximate analytical methods is needed for this. In this talk, I discuss how the binary dynamics and the emit-ted gravitational waves can be calculated within the post-Newtonian (weak-field and slow-motion) approximation. This can be formulated conveni-ently within an effective field-theory framework. The calculation can be performed by methods also used in particle physics (Feynman integrals) and be automated using computer algebra.

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.