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

TL;DR

Non-Abelian T-duality for SO(4) symmetric type II backgrounds is cast as consistent truncations to seven-dimensional supergravity, producing an invertible map between solutions of massive IIA and type IIB. The authors derive a universal 7D reduction on S^3 and show that its NATD dual on R×S^2 yields the same 7D theory, enabling uplift of any solution to both theories. Supersymmetry is shown to be halved for spinors transforming under the SU(2) used in the duality, via a spinor rotation and Kosmann derivative analysis. The framework is applied to explicit examples (pp-wave, LLM, Lifshitz), generating new massive IIA backgrounds and illustrating the invertible duality, with insights into D-brane dynamics and holographic interpretations. Overall, the work provides a solid, general method to generate and study non-Abelian T-duals in type II supergravity and their physical implications.

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.