Integrability, spin-chains and the AdS3/CFT2 correspondence

• Published in: The journal of high energy physics 2011-08, Vol.2011 (8), Article 29
• Main Authors: Sax, O. Ohlsson, Stefański, B.
• Format: Article
• Language: English
• Subjects: Chains; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2011)029

Building on arXiv:0912.1723 [ 1 ], in this paper we investigate the AdS 3 /CFT 2 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 CFT 2 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 AdS 3 /CFT 2 correspondence.