How to uplift non-maximal gauged supergravities

TL;DR

This paper introduces an algorithm for uplifting non-maximal gauged supergravities to higher-dimensional supergravities using exceptional field theory, simplifying the process to solving a PDE on a quotient space, and classifies all uplifts of a specific supergravity.

Contribution

It provides a new algorithm for consistent uplift of non-maximal supergravities and classifies all uplifts of a specific four-dimensional supergravity to type IIB.

Findings

Uplift consistency is equivalent to solving a PDE on a quotient space.

Classified all uplifts of SO(4)-gauged supergravity to type IIB.

Recovered known truncations around D'Hoker-Estes-Gutperle solutions.

Abstract

In this paper, we provide an algorithm to perform the uplift of non-maximal $G_g$-gauged supergravities to type IIB or 11D supergravities. Using tools of exceptional field theory and generalised geometry, we show that the internal manifold admits a $G_g$-action, and that consistency of the uplift is equivalent to solving a simpler PDE on the quotient $M_{\text{int}}/G_g$. As an application, we classify all possible uplifts of pure half-maximal four-dimensional $\textrm{SO}(4)$-gauged supergravity to type IIB and we recover consistent truncations around any of the D'Hoker-Estes-Gutperle solutions \cite{DHoker:2007hhe}.