Consistent Kaluza-Klein Truncations via Exceptional Field Theory

TL;DR

This paper develops a framework for consistent Kaluza-Klein truncations using exceptional field theory, enabling new compactifications on spheres and hyperboloids that produce diverse gauged supergravities.

Contribution

It introduces a generalized Scherk-Schwarz reduction ansatz with explicit twist matrices, extending the scope of consistent truncations to include non-homogeneous internal spaces.

Findings

Constructed explicit twist matrices satisfying consistency equations.

Derived gauged supergravities with SO(p,q) and CSO(p,q,r) gauge groups.

Extended the class of known compactifications to hyperboloids and warped spaces.

Abstract

We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO(p,q) and CSO(p,q,r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides $H^{p,q}$, thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D=11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS$_5\times S^5$), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.