Kaluza-Klein fermion mass matrices from Exceptional Field Theory and ${\cal N} =1$ spectra

TL;DR

This paper uses Exceptional Field Theory to compute the infinite-dimensional mass matrices and spectra of Kaluza-Klein fermions in M-theory and type IIA solutions with spherical internal spaces, revealing consistent spectral features.

Contribution

It introduces a method to determine the full fermionic Kaluza-Klein spectra for specific AdS solutions using Exceptional Field Theory, including both supersymmetric and non-supersymmetric cases.

Findings

Complete fermionic spectra for certain AdS solutions are obtained.

Spectra exhibit generic features across different solutions.

Results unify fermionic and bosonic spectra analysis.

Abstract

Using Exceptional Field Theory, we determine the infinite-dimensional mass matrices for the gravitino and spin-$1/2$ Kaluza-Klein perturbations above a class of anti-de Sitter solutions of M-theory and massive type IIA string theory with topologically-spherical internal spaces. We then use these mass matrices to compute the spectrum of Kaluza-Klein fermions about some solutions in this class with internal symmetry groups containing SU(3). Combining these results with previously known bosonic sectors of the spectra, we give the complete spectrum about some ${\cal N}=1$ and some non-supersymmetric solutions in this class. The complete spectra are shown to enjoy certain generic features.