Infinite and finite consistent truncations on deformed generalised parallelisations

TL;DR

This paper develops a method to construct new consistent truncations of supergravity theories on manifolds by using exceptional generalised geometry, enabling the inclusion of finite or infinite Kaluza-Klein mode sets.

Contribution

It introduces a framework for formulating both finite and infinite consistent truncations via deformed generalised parallelisations within exceptional generalised geometry.

Findings

Explicit embedding of known truncations into exceptional generalised geometry.

Construction of truncations involving infinite Kaluza-Klein mode towers.

Unified description of finite and infinite consistent truncations.

Abstract

Given a manifold $\mathbb{M}$ admitting a maximally supersymmetric consistent truncation, we show how to formulate new consistent truncations by restricting to a set of Kaluza-Klein modes on $\mathbb{M}$ invariant under some subgroup of the group of isometries of $\mathbb{M}$. These truncations may involve either finite or infinite sets of modes. We provide their global description using exceptional generalised geometry to construct a `deformed' generalised parallelisation starting with that on $\mathbb{M}$. This allows us to explicitly embed known consistent truncations directly into exceptional generalised geometry/exceptional field theory, and to obtain the equations governing situations where the consistent truncation retains an infinite tower of modes.