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

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.

17 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3: minor corrections, final version

References in corpus (8)

• Tailoring Three-Point Functions and Integrability
• A Shortcut to the Q-Operator
• Baxter Q-Operators and Representations of Yangians
• Review of AdS/CFT Integrability, Chapter VI.1: Superconformal Symmetry
• Oscillator Construction of su(n|m) Q-Operators
• Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills
• Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve
• Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability

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• Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills
• Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve
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