Generalised Scherk-Schwarz reductions from gauged supergravity

TL;DR

This paper presents a systematic method for constructing generalized Scherk-Schwarz uplifts of gauged supergravities, deriving internal manifolds, fluxes, and truncation Ansatz from the embedding tensor, and extends to torus fibrations.

Contribution

It introduces a new procedure to build generalized Scherk-Schwarz reductions from gauged supergravities using the embedding tensor, including a no-go theorem and extension to torus fibrations.

Findings

Recovered known Scherk-Schwarz reductions

Proved a no-go result for certain gaugings

Extended construction to torus fibrations

Abstract

A procedure is described to construct generalised Scherk-Schwarz uplifts of gauged supergravities. The internal manifold, fluxes, and consistent truncation Ansatz are all derived from the embedding tensor of the lower-dimensional theory. We first describe the procedure to construct generalised Leibniz parallelisable spaces where the vector components of the frame are embedded in the adjoint representation of the gauge group, as specified by the embedding tensor. This allows us to recover the generalised Scherk-Schwarz reductions known in the literature and to prove a no-go result for the uplift of $\omega$-deformed SO(p,q) gauged maximal supergravities. We then extend the construction to arbitrary generalised Leibniz parallelisable spaces, which turn out to be torus fibrations over manifolds in the class above.