String theories on warped AdS backgrounds and integrable deformations of spin chains

TL;DR

This paper explores integrable deformations of AdS/CFT involving warped AdS_3 geometries, deriving corresponding sigma models and connecting them to deformed spin chains, thus advancing understanding of string backgrounds and integrable systems.

Contribution

It introduces new integrable deformations of AdS_3 geometries and establishes their correspondence with deformed spin chains through Landau-Lifshitz sigma models.

Findings

Warped AdS_3 geometries are embedded into type IIB supergravity solutions.

Deformed spin chains correspond to anisotropic and Jordanian deformations.

Continuum limits of spin chains match Landau-Lifshitz sigma models from string theory.

Abstract

We study integrable deformations of AdS/CFT by focusing upon three kinds of warped AdS_3 geometries, 1) space-like warped AdS_3, 2) time-like warped AdS_3 and 3) null warped AdS_3. These geometries are embedded into type IIB supergravity solutions and are regarded as consistent string backgrounds. By restricting the classical motion of strings on the warped AdS_3xS^1 subspace, the Landau-Lifshitz sigma models are derived by taking the fast-moving limit. The first two warped AdS_3 spaces correspond to anisotropic deformations of the sl(2) spin chain and the last one to Jordanian deformations. After taking the continuum limit of the deformed spin chains with coherent states, the resulting theories agree with the Landau-Lifshitz sigma models obtained from the string-theory side.