Spectral sum rules and finite volume partition function in gauge theories with real and pseudoreal fermions

TL;DR

This paper derives sum rules for the eigenvalues of the QCD Dirac operator in finite volume gauge theories with real and pseudoreal fermions, linking chiral symmetry breaking patterns to spectral properties.

Contribution

It provides a derivation of fermion mass dependence of the partition function and eigenvalue sum rules based on chiral symmetry breaking, confirming earlier random matrix theory results.

Findings

Sum rules match those from random matrix theory.

Results apply to $N_c=2$ and Yang-Mills with light adjoint Majorana fermions.

Clarifies spectral properties in theories with real and pseudoreal fermions.

Abstract

Based on the chiral symmetry breaking pattern and the corresponding low-energy effective lagrangian, we determine the fermion mass dependence of the partition function and derive sum rules for eigenvalues of the QCD Dirac operator in finite Euclidean volume. Results are given for $N_c = 2$ and for Yang-Mills theory coupled to several light adjoint Majorana fermions. They coincide with those derived earlier in the framework of random matrix theory.