On the squashed seven-sphere operator spectrum

Abstract

We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in $Ad{S}_4$ and are important for the corresponding $\mathcal{N}=1$ supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in $Ad{S}_4$ was derived for this compactification. Some comments are also made concerning the $G_2$ holonomy and its implications on the structure of the operator equations on the squashed seven-sphere.

28 pages, v2: typos corrected, a footnote added

References in corpus (2)

• The String Landscape and the Swampland
• Supersymmetric spectroscopy on AdS${}_4\times S^7$ and AdS${}_4\times S^6$

Cited by in corpus (2)

• Kaluza-Klein Spectrometry beyond Consistent Truncations: The Squashed $S^7$
• Compactifications of String/M-Theory and the Swampland: A Study of the AdS${}_{\text{4}}$ Mass Spectrum of Eleven-Dimensional Supergravity on the Squashed Seven-Sphere