# Unimodular jordanian deformations of integrable superstrings

## TL;DR

This paper introduces new unimodular jordanian r matrices with supercharges, leading to novel superstring backgrounds that satisfy supergravity equations, and reveals their relation to non-abelian T duality and TsT transformations.

## Contribution

It presents the first construction of unimodular jordanian r matrices with supercharges for superstring deformations, expanding the landscape of integrable backgrounds.

## Key findings

- Derived new supergravity solutions from jordanian r matrices.
- Established equivalence of deformations to non-abelian T duality.
- Identified backgrounds related to TsT and S duality transformations.

## Abstract

We find new homogeneous r matrices containing supercharges, and use them to find new backgrounds of Yang-Baxter deformed superstrings. We obtain these as limits of unimodular inhomogeneous r matrices and associated deformations of AdS2 x S2 x T6 and AdS5 x S5. Our r matrices are jordanian, but also unimodular, and lead to solutions of the regular supergravity equations of motion. In general our deformations are equivalent to particular non-abelian T duality transformations. Curiously, one of our backgrounds is also equivalent to one produced by TsT transformations and an S duality transformation.