# Two-parameter integrable deformations of the $AdS_3 \times S^3 \times T^4$ superstring

## TL;DR

This paper introduces a two-parameter integrable deformation of the $AdS_3 imes S^3 imes T^4$ superstring, analyzing its symmetries, fluxes, and supergravity solutions, expanding the landscape of integrable string backgrounds.

## Contribution

It develops a novel two-parameter deformation framework for superstrings on $AdS_3 imes S^3 imes T^4$, including explicit supergravity backgrounds and their limits.

## Key findings

- Constructed two supergravity backgrounds for the deformed superstring.
- Analyzed kappa-symmetry and flux formulas for the deformation.
- Compared solutions to existing literature and generalized supergravity equations.

## Abstract

For supercosets with isometry group of the form $\hat{G} \times \hat{G}$, the eta-deformation can be generalised to a two-parameter integrable deformation with independent $q$-deformations of the two copies. We study its kappa-symmetry and write down a formula for the Ramond-Ramond fluxes. We then focus on $\hat{G}= PSU(1,1|2)$ and construct two supergravity backgrounds for the two-parameter integrable deformation of the $AdS_3 \times S^3 \times T^4$ superstring, as well as explore their limits. We also construct backgrounds that are solutions of the weaker generalised supergravity equations of motion and compare them to the literature.