Dirac Spectra of 2-dimensional QCD-like theories

TL;DR

This paper classifies Dirac spectra of 2D QCD-like theories using random matrix theory, confirming predictions with lattice simulations and exploring implications for symmetry and disorder in low-dimensional systems.

Contribution

It provides a novel classification of Dirac spectra in 2D QCD-like theories based on their symmetries, differing from 4D QCD, and confirms these with lattice data.

Findings

Spectra classification depends on lattice parity.

Agreement with random matrix theory predictions.

Implications for symmetry and disorder in 2D systems.

Abstract

We analyze Dirac spectra of two-dimensional QCD like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The classification is different from QCD in four dimensions because the anti-unitary symmetries do not commute with $\gamma_5$. Therefore in a chiral basis, the number of degrees of freedom per matrix element are not given by the Dyson index. Our predictions are confirmed by Dirac spectra from quenched lattice simulations for QCD with two or three colors with quarks in the fundamental representation as well as in the adjoint representation. The universality class of the spectra depends on the parity of the number of lattice points in each direction. Our results show an agreement with random matrix theory that is qualitatively similar to the agreement found for QCD in four dimensions. We discuss the implications for the Mermin-Wagner-Coleman theorem and put our results in the context of two-dimensional disordered systems.