On T-duality transformations for the three-sphere

TL;DR

This paper explores T-duality transformations on the three-sphere with H-flux, developing a new non-abelian T-duality method that yields primarily geometric backgrounds, contrasting with expectations of non-geometric results.

Contribution

It introduces a novel procedure for non-abelian T-duality on the three-sphere, providing an alternative perspective and highlighting the geometric nature of the resulting backgrounds.

Findings

Transformations mostly produce geometric backgrounds

Develops a new non-abelian T-duality method

Contrasts with previous expectations of non-geometric outcomes

Abstract

We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting backgrounds turn out to be geometric in nature. To perform the duality transformations, we develop a novel procedure for non-abelian T-duality, which follows a route different compared to the known literature, and which highlights the underlying structure from an alternative point of view.