Kaluza-Klein trombone mass matrices and universal class $\mathcal{R}$ operator spectra

TL;DR

This paper identifies universal light operator spectra in a class of superconformal field theories using holographic Kaluza-Klein spectral analysis on known AdS backgrounds, focusing on the role of trombone gaugings.

Contribution

It derives and diagonalizes Kaluza-Klein mass matrices for gaugings of the trombone symmetry, revealing universal spectra in superconformal theories of class R.

Findings

Universal sectors of light operator spectrum are identified across all theories in the class.

Kaluza-Klein mass matrices are explicitly derived and diagonalized for trombone gaugings.

A prescription is provided to isolate globally-defined universal spectra.

Abstract

We determine universal sectors of the light operator spectrum that are present in all A$_{N-1}$ superconformal field theories $T_N[\Sigma_3]$ of class $\mathcal{R}$, with $\Sigma_3$ a compact hyperbolic three-manifold. We do this at large $N$ by holographically mapping the problem to a Kaluza-Klein spectral analysis over previously known dual anti-de Sitter backgrounds related to wrapped M5-brane configurations. Associated to these, $D=4$ $\mathcal{N}=8$ supergravities have been recently constructed that allow for the application of spectral techniques based on exceptional generalised geometry/field theory. We derive the Kaluza-Klein mass matrices that arise when the seed lower-dimensional maximal supergravity involves gaugings of the trombone scaling symmetry, as pertains to the case at hand, and diagonalise them to find the universal Kaluza-Klein states. In general, these universal spectra are only defined locally, and we give a prescription to isolate globally-defined sectors therein.