Spectral sum rules for confining large-N theories

TL;DR

This paper investigates spectral sum rules in large-N gauge theories with adjoint matter on squashed three-spheres, revealing potential universal properties in the confined phase at weak coupling.

Contribution

It introduces conjectured universal spectral sum rules for large-N gauge theories with massive adjoint matter on squashed three-spheres at vanishing coupling.

Findings

Spectral sums are analyzed in the weak coupling limit.

Results suggest possible universal spectral sum rules.

The study provides insights into the spectral structure of large-N theories.

Abstract

We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing 't Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale $\Lambda^{-1}$. Our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.