A review of integrable deformations in AdS/CFT

TL;DR

This paper reviews integrable deformations of AdS/CFT backgrounds, focusing on their classical integrability, Bethe equations, and spectral properties, highlighting recent advances in understanding these deformations within string theory.

Contribution

It provides a comprehensive review of integrable deformations of AdS_5 and S^5, emphasizing the derivation of Bethe equations and their role in classical integrability.

Findings

String spectra match Bethe equation predictions in the near-pp-wave limit.

Bethe equations can be derived using Lax pairs and Riemann-Hilbert methods.

Deformations preserve classical integrability of the string background.

Abstract

Marginal beta deformations of N=4 super-Yang-Mills theory are known to correspond to a certain class of deformations of the S^5 background subspace of type IIB string theory in AdS_5 x S^5. An analogous set of deformations of the AdS_5 subspace is reviewed here. String energy spectra computed in the near-pp-wave limit of these backgrounds match predictions encoded by discrete, asymptotic Bethe equations, suggesting that the twisted string theory is classically integrable in this regime. These Bethe equations can be derived algorithmically by relying on the existence of Lax representations, and on the Riemann-Hilbert interpretation of the thermodynamic Bethe ansatz. This letter is a review of a seminar given at the Institute for Advanced Study, based on research completed in collaboration with McLoughlin.