Integrability, spin-chains and the AdS3/CFT2 correspondence

TL;DR

This paper develops an all-loop Bethe Ansatz for strings on AdS3 x S^3 x S^3 x S^1, incorporating massless modes and providing insights into the dual CFT2, using integrability techniques and novel alpha-dependent mappings.

Contribution

It introduces a new alpha-dependent Bethe Ansatz and spin-chain models for AdS3/CFT2, including massless modes, advancing the understanding of the duality's integrable structure.

Findings

All-loop Bethe Ansatz valid for all alpha values.

Construction of integrable spin-chains corresponding to weak coupling.

Non-singular limit as alpha approaches 1, capturing massless modes.

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.