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Letters in Mathematical Physics

, Volume 99, Issue 1–3, pp 191–208 | Cite as

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

  • Matthias Staudacher
Article

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.

Mathematics Subject Classification (2010)

82B23 16T25 

Keywords

Bethe ansatz R-matrix Q-operator 

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Copyright information

© Springer 2011

Authors and Affiliations

  1. 1.Institut für Mathematik und Institut für PhysikHumboldt-Universität zu Berlin, Johann von Neumann-HausBerlinGermany
  2. 2.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutPotsdamGermany

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