Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix 
Formalism

Staudacher, Matthias

doi:10.1007/s11005-011-0530-9

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Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism

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Staudacher, Matthias
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Staudacher, M. (2012). Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism. Letters in Mathematical Physics, 99(1-3), 191-208. doi:10.1007/s11005-011-0530-9.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-E683-7

Abstract

The one-dimensional 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 Q-operator of the XXX chain. It allows to find the spectrum of the model using certain algebraic techniques, while entirely avoiding Bethe's ansatz.