Kaluza-Klein Spectrometry beyond Consistent Truncations: The Squashed $S^7$

TL;DR

This paper demonstrates how to use Exceptional Field Theory to compute complete Kaluza-Klein spectra for deformed supergravity backgrounds, including non-truncation modes, exemplified by the squashed S^7.

Contribution

It introduces a method to determine full spectra beyond consistent truncations using Exceptional Field Theory, applied to squashed S^7 backgrounds.

Findings

Computed full Kaluza-Klein spectrum of squashed S^7

Derived a universal formula for conformal dimensions

Extended analysis to non-truncation scalar modes

Abstract

We show how to use Exceptional Field Theory to compute the full Kaluza-Klein spectra of 10- and 11-dimensional supergravity around deformations of backgrounds of maximal gauged supergravity by scalar modes that do not form part of the consistent truncation. This includes deformations of AdS$_4 \times S^7$ and AdS$_5 \times S^5$ by modes that are not part of the ${\cal N}=8$ supermultiplet. As an application, we compute the full Kaluza-Klein spectrum of the ${\cal N}=1$ and ${\cal N}=0$ squashed $S^7$. In this example, all conformal dimensions are captured by a universal formula in terms of the Casimir operators and additional quantum numbers which organise the spectrum.