Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions

TL;DR

This paper derives the microscopic spectral correlators of the Dirac operator in three-dimensional QCD using supersymmetric methods, providing new determinant formulas that align with random matrix theory predictions.

Contribution

It introduces a supersymmetric formulation to compute spectral correlators in 3D QCD and extends random matrix theory results to this setting.

Findings

Derived new determinant expressions for spectral correlators.

Confirmed agreement with random matrix theory predictions.

Extended spectral analysis from 4D to 3D QCD.

Abstract

The microscopic spectral correlators of the Dirac operator in three-dimensional Yang-Mills theory coupled to fundamental fermions and with three or more colours are derived from the supersymmetric formulation of partially quenched effective Lagrangians. The flavour supersymmetry breaking patterns are appropriately identified and used to calculate the corresponding finite volume partition functions from Itzykson-Zuber type integrals over supersymmetric cosets. New and simple determinant expressions for the spectral correlators in the mesoscopic scaling region are thereby found. The microscopic spectrum derived from the effective finite volume partition function of three-dimensional QCD agrees with earlier results based on the unitary ensemble of random matrix theory and extends the corresponding calculations for QCD in four dimensions.