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

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 $\mathcal{N}=8$ supermultiplet. As an application, we compute the full Kaluza-Klein spectrum of the $\mathcal{N}=1$ and $\mathcal{N}=0$ 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.

arXiv comment27 pages. v2: minor changes and added fermionic spectra of $\mathcal{N}=0$ squashed $S^7$. v3: typos corrected

References in corpus (27)

• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Einstein manifolds and conformal field theories
• Exceptional Form of D=11 Supergravity
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• The gauge structure of generalised diffeomorphisms
• Exceptional Field Theory II: E${}_{7(7)}$
• The maximal D=4 supergravities
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Spectrum of Type IIB Supergravity on AdS_5 x T^{11}: Predictions on N = 1 SCFT's
• Spin-2 spectrum of defect theories
• Kaluza-Klein Spectrometry for Supergravity
• Kaluza-Klein Spectrometry from Exceptional Field Theory
• Stable non-supersymmetric Anti-de Sitter vacua of massive IIA supergravity
• Holographic Evidence for Non-Supersymmetric Conformal Manifolds
• Tachyonic Kaluza-Klein modes and the AdS swampland conjecture
• Global Properties of the Conformal Manifold for S-Fold Backgrounds
• S-folds and holographic RG flows on the D3-brane
• Kaluza-Klein fermion mass matrices from Exceptional Field Theory and $\mathcal{N}=1$ spectra
• The spectrum of marginally-deformed $\mathcal{N}=2$ CFTs with AdS${}_4$ S-fold duals of type IIB
• Kaluza-Klein Spectroscopy for the Leigh-Strassler SCFT
• The role of singletons in $S^7$ compactifications
• Supersymmetric spectroscopy on AdS${}_4\times S^7$ and AdS${}_4\times S^6$
• Super-Chern-Simons spectra from Exceptional Field Theory
• Marginal deformations from type IIA supergravity
• On the squashed seven-sphere operator spectrum
• On the Superconformal Index of Chern-Simons theories and their KK Spectrometry
• Exactly Marginal Deformations and their Supergravity Duals

Cited by in corpus (3)

• Infinite and finite consistent truncations on deformed generalised parallelisations
• Charting the Conformal Manifold of Holographic CFT${}_2$'s
• De-Higgsing In Eleven-Dimensional Supergravity On The Squashed $S^7$