Supersymmetry and integrability of the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ superstring

TL;DR

This paper constructs a supersymmetric, integrable elliptic deformation of the $ ext{AdS}_3 imes ext{S}^3 imes ext{T}^4$ superstring with Ramond-Ramond flux, analyzing its S-matrix and classical integrability properties.

Contribution

It introduces a one-parameter family of deformations supporting the background, computes the worldsheet S-matrix, and provides evidence for integrability and supersymmetry in the deformed model.

Findings

S-matrix satisfies the classical Yang-Baxter equation

Deformation preserves 8 supercharges

Limits include trigonometric deformations and $ ext{AdS}_2 imes ext{S}^2 imes ext{T}^6$

Abstract

We construct a 1-parameter family of Ramond-Ramond fluxes supporting the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ metric with constant dilaton and preserving 8 of the 16 supercharges of the undeformed background. On the supersymmetric locus, we compute the tree-level worldsheet S-matrix in uniform light-cone gauge up to quadratic order in fermions and find that it non-trivially satisfies the classical Yang-Baxter equation. Moreover, imposing classical integrability and symmetries, we conjecture compatible processes quartic in fermions. We also investigate different limits of interest, including trigonometric deformations and the limit to the $\mathrm{AdS}_2 \times \mathrm{S}^2 \times \mathrm{T}^6$ superstring. Our results provide strong evidence for a supersymmetric and integrable elliptic deformation of the $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ superstring supported by Ramond-Ramond flux and a constant dilaton.