7-dimensional ${\cal N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory

TL;DR

This paper develops a method to construct consistent seven-dimensional supergravity truncations from higher-dimensional theories using $ ext{SL}(5)$ exceptional field theory, with conditions expressed geometrically and related to intrinsic torsion.

Contribution

It introduces a geometric framework for consistent truncations on generalised $ ext{SU}(2)$-structure manifolds within $ ext{SL}(5)$ exceptional field theory, linking embedding tensors to intrinsic torsion.

Findings

Truncations are defined on generalised $ ext{SU}(2)$-structure manifolds.

Embedding tensor corresponds to intrinsic torsion of generalised $ ext{SU}(2)$-connections.

Consistency conditions are expressed via the generalised Lie derivative.

Abstract

We show how to construct seven-dimensional half-maximally supersymmetric consistent truncations of 11-/10-dimensional SUGRA using $\mathrm{SL}(5)$ exceptional field theory. Such truncations are defined on generalised $\mathrm{SU}(2)$-structure manifolds and give rise to seven-dimensional half-maximal gauged supergravities coupled to $n$ vector multiplets and thus with scalar coset space $\mathbb{R}^+ \times \mathrm{O}(3,n)/\mathrm{O}(3)\times\mathrm{O}(n)$. The consistency conditions for the truncation can be written in terms of the generalised Lie derivative and take a simple geometric form. We show that after imposing certain "doublet" and "closure" conditions, the embedding tensor of the gauged supergravity is given by the intrinsic torsion of generalised $\mathrm{SU}(2)$-connections and automatically satisfies the linear constraint of seven-dimensional half-maximal gauged supergravities, as well as the quadratic constraint when the section condition is satisfied.