Integrable supersymmetric deformations of $\rm AdS_3 \times S^3 \times T^4$

TL;DR

This paper constructs integrable deformations of the $ m AdS_3 imes S^3 imes T^4$ background in type IIB string theory, preserving supersymmetry and integrability through a combination of dualities and Yang-Baxter deformations.

Contribution

It introduces a new class of integrable, supersymmetric string backgrounds obtained via dualities and Yang-Baxter deformations, preserving classical integrability.

Findings

Deformed backgrounds preserve 8 supercharges.

Integrability is maintained despite S-duality transformations.

Deformations relate to an inhomogeneous Yang-Baxter model.

Abstract

We construct a family of type IIB string backgrounds that are deformations of $\rm AdS_3 \times S^3 \times T^4$ with a "squashed" $\rm AdS_3 \times S^3$ metric supported by a combination of NSNS and RR fluxes. They have global $\rm SU(1,1) \times SU(2)$ symmetry, regular curvature, constant dilaton and preserve 8 supercharges. Upon compactification to 4 dimensions they reduce to $\mathcal N=2$ supersymmetric $\rm AdS_2 \times S^2$ solutions with electric and magnetic Maxwell fluxes. These type IIB supergravity solutions can be found from the undeformed $\rm AdS_3 \times S^3 \times T^4$ background by a combination of T-dualities and S-duality. In contrast to T-duality, S-duality transformations of a type IIB supergravity background do not generally preserve the classical integrability of the corresponding Green-Schwarz superstring sigma model. Nevertheless, we show that integrability is preserved in the present case. Indeed, we find that these backgrounds can be obtained, up to T-dualities, from an integrable inhomogeneous Yang-Baxter deformation (with unimodular Drinfel'd-Jimbo R-matrix) of the original $\rm AdS_3 \times S^3$ supercoset model.