Massive Spectral Sum Rules for the Dirac Operator

TL;DR

This paper derives massive spectral sum rules for Dirac operators in gauge theories, confirming their consistency with known random matrix theory spectral densities, thus advancing understanding of spectral properties in quantum chromodynamics.

Contribution

It introduces new massive spectral sum rules for Dirac operators in gauge theories, linking them with random matrix theory results.

Findings

Sum rules are consistent with random matrix theory spectral densities.

Provides a universal framework for spectral analysis in gauge theories.

Enhances understanding of spectral properties in quantum chromodynamics.

Abstract

Massive spectral sum rules are derived for Dirac operators of $SU(N_c)$ gauge theories with $N_f$ flavors. The universal microscopic massive spectral densities of random matrix theory, where known, are all consistent with these sum rules.