Supersymmetric spectroscopy on AdS$_4\times S^7$ and AdS$_4\times S^6$

TL;DR

This paper computes the complete Kaluza-Klein spectra of five supersymmetric AdS$_4$ solutions in eleven-dimensional and type IIA supergravity, using new techniques based on Exceptional Field Theory, thus completing the spectra for known solutions.

Contribution

It provides the full Kaluza-Klein spectra for five specific AdS$_4$ solutions, expanding the understanding of their supersymmetric spectra using advanced computational methods.

Findings

Complete spectra for five AdS$_4$ solutions in supergravity.

Solutions preserve specific internal symmetries like SO(3) and U(1).

Results exhaust known supersymmetric AdS$_4$ spectra in the studied class.

Abstract

New techniques based on Exceptional Field Theory have recently allowed for the calculation of the Kaluza-Klein spectra of certain AdS$_4$ solutions of $D=11$ and massive IIA supergravity. These are the solutions that consistently uplift on $S^7$ and $S^6$ from vacua of maximal four-dimensional supergravity with SO(8) and ISO(7) gaugings. In this paper, we provide the complete Kaluza-Klein spectrum of five such AdS$_4$ solutions, all of them ${\cal N}=1$. These solutions preserve SO(3) and $\textrm{U}(1) \times \textrm{U}(1)$ internal symmetry in $D=11$, and U(1) (two of them) and no continuous symmetry in type IIA. Together with previously discussed cases, our results exhaust the Kaluza-Klein spectra of known supersymmetric AdS$_4$ solutions in $D=11$ and type IIA in the relevant class.