Integrability, spin-chains and the AdS(3)/CFT2 correspondence

Sax, O. O. & Stefanski, B. (2011). Integrability, spin-chains and the AdS(3)/CFT2 correspondence. Journal of High Energy Physics, 2011(8), doi: 10.1007/JHEP08(2011)029

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Abstract

Building on arXiv:0912.1723, 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 x S^3 x S^3 x S^1, with symmetry D(2,1;alpha)^2, valid for all values of alpha. This construction relies on a novel, alpha-dependent generalisation of the Zhukovsky map. We investigate the weakly-coupled limit of this BA and of the all-loop BA for strings on AdS_3 x S^3 x 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 x S^3 x S^3 x S^1. We show that, in the alpha to 1 limit, the integrable structure of the D(2,1;alpha) 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.

Item Type: Article
Uncontrolled Keywords: Gauge-gravity correspondence, AdS-CFT Correspondence, ANALYTIC BETHE-ANSATZ, LIE SUPERALGEBRA SL(R+1-VERTICAL-BAR-S+1), SL(2,R) WZW MODEL, FUNCTIONAL-EQUATIONS, ANOMALOUS DIMENSION, BRANE INTERSECTIONS, SUPERSTRING ACTION, STRING THEORY, GAUGE-THEORY, S-MATRIX
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/998

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