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Integrability, spin-chains and the AdS3/CFT2 correspondence

  • O. Ohlsson Sax
  • B. StefańskiJr.
Article

Abstract

Building on arXiv:0912.1723 [1], in this paper we investigate the AdS3/CFT2 correspondence using integrability techniques. We present an all-loop Bethe Ansatz (BA) for strings on AdS 3 × S 3 × S 3 × S 1, with symmetry d(2, 1; α)2, valid for all values of α. This construction requires an α-dependent scaling of the Zhukovsky map. We investigate the weakly-coupled limit of this BA and of the all-loop BA for strings on AdS 3 × S 3 × T 4. We construct integrable short-range spin-chains and Hamiltonians that correspond to these weakly-coupled BAs. The spin-chains are alternating and homogenous, respectively. The alternating spin-chain can be regarded as giving some of the first hints about the unknown CFT2 dual to string theory on AdS 3 × S 3 × S 3 × S 1. We show that, in the α → 1 limit, the integrable structure of the d(2, 1; α)2 model is non-singular and keeps track of not just massive but also massless modes. This provides a way of incorporating massless modes into the integrability machinery of the AdS3/CFT2 correspondence.

Keywords

Gauge-gravity correspondence AdS-CFT Correspondence 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUppsala UniversityUppsalaSweden
  2. 2.Centre for Mathematical ScienceCity University LondonLondonU.K.

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