Non-Abelian T-duality and consistent truncations in type-II supergravity

TL;DR

This paper explores how non-Abelian T-duality acts on SO(4) symmetric backgrounds in type II supergravity, establishing a consistent truncation framework that relates solutions in massive IIA and IIB theories, and analyzing supersymmetry breaking effects.

Contribution

It introduces a consistent truncation approach for non-Abelian T-duality in SO(4) symmetric backgrounds, linking solutions across massive IIA and IIB supergravities and examining supersymmetry implications.

Findings

Non-Abelian T-duality can be described via consistent truncation to 7D theories.

Any solution in these theories uplifts to both massive IIA and IIB supergravities.

Non-Abelian T-duality breaks half of the supersymmetry for SO(4) spinors.

Abstract

For a general class of SO(4) symmetric backgrounds in type II-supergravity, we show that the action of non-Abelian T-duality can be described via consistent truncation to seven dimensional theories with seemingly massive modes. As such, any solution to these theories uplifts to both massive type IIA and IIB supergravities presenting an invertible map between the two. For supersymmetric backgrounds, we show that for spinors transforming under SO(4) the non-Abelian T-duality transformation breaks the original supersymmetry by half. We use these mappings to generate the non-Abelian T-duals of the maximally supersymmetric pp-wave, the Lin, Lunin, Maldacena geometries and spacetimes with Lifshitz symmetry.