Random matrix theory and $QCD_3$

TL;DR

This paper links the spectral properties of three-dimensional QCD near zero virtuality to a Hermitean random matrix model, deriving exact spectral densities and new sum rules, and discussing anomalies in such models.

Contribution

It introduces a Hermitean random matrix model for 3D QCD spectral properties, deriving exact densities and sum rules, and addressing anomalies.

Findings

Exact spectral density derived for even and odd fermion numbers.

New sum rules for inverse eigenvalues of the Dirac operator.

Discussion on anomalies in random matrix theories.

Abstract

We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number of fermions. New sum rules for the inverse powers of the eigenvalues of the Dirac operator are obtained. The issue of anomalies in random matrix theories is discussed.