Integrability, spin-chains and the AdS3/CFT2 correspondence

By O. O. Sax, Bogdan Stefański. 2011

150 citations recorded by the source corpus.

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 AdS3 × S3 × S3 × S1, 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 AdS3 × S3 × T4. 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 AdS3 × S3 × S3 × S1. 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cda882abfd009de1c90cb19ea78ce6553393dfd0

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Citations in the corpus

Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “After some initial investigations based on semiclassical integrability properties [168, 169], these were fixed in refs.”
Higher spins & strings (2014, background): “stem away from the symmetric product point without the need of having to concentrate on BPS protected quantities. Any relationship here to the integrability of the string worldsheet theory, see e.g., [74, 75] and [76] for a recent review, may also be useful for this. One might also take encouragemen”
A dynamic $ su{(1|1)^2} $ S-matrix for AdS3/CFT2 (2012, methodology): “Furthermore, some of these phases yield non-trivial scattering processes between modes of different mass that were not accounted for in [6, 10].”
The complete worldsheet S matrix of superstrings on AdS3×S3×T4 with mixed three-form flux (2014, background): “While the massive excitations could be investigated [15–26] using more conventional integrability methods developed in the context of AdS5/CFT4 and AdS4/CFT3, massless modes appeared initially to be rather different and difficult to incorporate fully into the holographic integrability approach.”
The all-loop integrable spin-chain for strings on AdS3 × S3 × T4: the massive sector (2013, background): “The integrable S-matrix that we have found depends on two undetermined antisymmetric phases Spq and S̃pq, which we now want to constrain.”