Gravitational analog of the Non-Abelian T-duality

TL;DR

This paper introduces a gravitational analog of non-abelian T-duality that works uniformly for all sphere dimensions and explores non-abelian TsT transformations for supergravity solutions.

Contribution

It proposes a new gravitational counterpart to NATD applicable to all spheres and a non-abelian TsT transformation for continuous geometry deformations.

Findings

The gravitational NATD reproduces the decompactification limit for all spheres.

The new transformations generate novel supergravity solutions with specific geometric factors.

The approach extends the applicability of duality transformations beyond previous limitations.

Abstract

Non-abelian T duality (NATD) is a symmetry of the worldsheet action that allows one to generate new solutions of string theory by performing algebraic transformations of known geometries. Applications of such transformations to spheres have been especially fruitful in the past, but the results did not reduce to the abelian transformation in the decompactification limit unless the dimension of sphere was equal to three. We propose a unique counterpart of NATD in classical gravity that reproduces the correct decompactification limit for all spheres $S^n$ but generates an n-form field strength and therefore cannot be naturally embedded in a worldsheet theory of NS-NS fields unless n=3. We also propose a non-abelian version of the TsT transformation which produces solutions of type II supergravity describing continuous deformations of geometries with $S^n\times S^n$ and $S^n\times T^n$ factors.