Kaluza-Klein Spectrometry from Exceptional Field Theory

Abstract

Exceptional field theories yield duality-covariant formulations of higher-dimensional supergravity. They have proven an efficient tool for the construction of consistent truncations around various background geometries. In this paper, we demonstrate how the formalism can moreover be turned into a powerful tool for computing the Kaluza-Klein mass spectra around these backgrounds. Most of these geometries have little to no remaining symmetries and their spectra are accessible to standard methods only in selected subsectors. The present formalism not only grants access to the full Kaluza-Klein spectra but also provides the scheme to identify the resulting mass eigenstates in higher dimensions. As a first illustration, we re-derive in compact form the mass spectrum of IIB supergravity on S 5 . We further discuss the application of our formalism to determine the mass spectra of higher Kaluza-Klein multiplets around the warped geometries corresponding to some prominent N = 2 and N = 0 AdS vacua in maximal supergravity.

Stable non-supersymmetric Anti-de Sitter vacua of massive IIA supergravity

“…[10], used to be notoriously difficult. However, within the last year, a new and powerful method based on Exceptional Field Theory (ExFT) [11] was developed in [12,13] for computing Kaluza-Klein spectra of vacua of maximal gauged supergravities. At the same time, [14] showed that probe branes can be used to easily search for signals, dubbed brane-instabilities, of non-perturbative instabilities [10].…”

“…In [12,13], ExFT was used to derive mass matrices for the Kaluza-Klein spectrum around any vacuum of N = 8 gauged supergravities in four and five dimensions that arises from a consistent truncation of 10-/11-dimensional supergravity. Let us briefly review some of the salient features of ExFT and Kaluza-Klein spectroscopy.…”

“…As shown in [12,13], a general Kaluza-Klein fluctuation around a vacuum that uplifts from four-dimensional gauged supergravity can be expressed as a product of the modes of the consistent truncation, with a complete basis of functions on the compactification manifold. A powerful feature of this method is that this complete basis of functions can be chosen to be the scalar harmonics, Y Σ , of the compactification with a metric that preserves the largest possible symmetry group, G max , in the lowerdimensional gauged supergravity.…”

“…The mass matrices are obtained by linearizing the ExFT field equations with the fluctuation ansatz (2) [12,13]. For the purpose of this letter, we give the scalar mass matrix in a yet more compact form:…”

Triality and the consistent reductions on ${\rm AdS}_3\times S^3$

“…Specifically, it is encoded in a group-valued Scherk-Schwarz twist matrix living on the duality group of the lowerdimensional theory. This formulation moreover allows a straightforward access to computing the entire Kaluza-Klein spectrum around any background living within the consistent truncation [12,13].…”