Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the RMatrix Formalism
Matthias Staudacher
Staudacher
Matthias
Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the RMatrix Formalism
Matthias Staudacher
MSC 2000
 16W30 Coalgebras, bialgebras, Hopf algebras ; rings, modules, etc. on which these act

82B23 Exactly solvable models; Bethe ansatz
Abstract
The onedimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the coordinate and the algebraic Bethe ansatz, giving reference to literature suitable for learning these techniques. Finally we speculate which of the methods might lift to the exact solution of the AdS/CFT system, and sketch a promising method for constructing the Baxter Qoperator of the XXX chain. It allows to find the spectrum of the model using certain algebraic techniques, while entirely avoiding Bethe's ansatz.
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