Dirac Spectrum in Adjoint QCD

TL;DR

This paper derives exact analytical results for the low-lying Dirac spectrum in adjoint QCD, linking spectral density slopes to chiral symmetries and extending the QCD partition function with ghost quarks.

Contribution

It provides a novel analytical expression for the spectral density slope in adjoint QCD using a supersymmetric generating function approach.

Findings

Analytical expression for the spectral density slope.

Consistency with scalar susceptibility results.

Extension of the QCD partition function with ghost quarks.

Abstract

In this lecture we discuss some exact results for the low-lying spectrum of the Dirac operator in adjoint QCD. In particular, we find an analytical expression for the slope of the average spectral density. These results are obtained by means of a generating function which is an extension of the QCD partition function with fermionic and bosonic ghost quarks. The low-energy limit of this generating function is completely determined by chiral (super-)symmetries. Our results for the slope of the average spectral density are consistent with the results for the scalar susceptibility which can be obtained from the usual chiral Lagrangian.