Consistent $\mathcal{N}=4$, $D=4$ truncation of type IIB supergravity on $\textrm{S}^{1} \times \textrm{S}^{5}$

TL;DR

This paper introduces a new method using Generalised Geometry and Exceptional Field Theory to identify consistent subsectors of four-dimensional gauged supergravities that can be embedded in higher-dimensional supergravity, exemplified by a truncation of type IIB supergravity.

Contribution

It develops a novel approach to find consistent truncations of supergravity theories based on structure group invariance, providing explicit uplift formulas for type IIB supergravity on S^1 x S^5.

Findings

A new method for consistent truncations using structure group invariance.

Explicit uplift formulas for type IIB supergravity on S^1 x S^5.

Demonstration of a consistent truncation to , D=4 supergravity.

Abstract

Fetching techniques from Generalised Geometry and Exceptional Field Theory, we develop a new method to identify consistent subsectors of four-dimensional gauged maximal supergravities that possess a (locally) geometric embedding in type IIB or 11D supergravity. We show that a subsector that is invariant under a structure group $\textrm{G}_\textrm{S} \subset \textrm{E}_{7(7)}$ can define a consistent truncation, even when $\textrm{G}_\textrm{S}$ is not part of the symmetry of the gauged maximal supergravity. As an illustration of the method, type IIB supergravity on $\textrm{S}^{1} \times \textrm{S}^{5}$ is shown to admit a consistent truncation to pure $\mathcal{N}=4$, $D=4$ gauged supergravity. Explicit uplift formulae are presented which provide a type IIB alternative to the M-theory embedding constructed by Cvetic, Lu and Pope $25$ years ago.