Bilinear condensate in three-dimensional large-$N_c$ QCD

TL;DR

This paper provides numerical evidence for a bilinear condensate in three-dimensional large-$N_c$ QCD, using a random matrix model to analyze eigenvalues of the overlap Dirac operator, estimating the condensate's value.

Contribution

It introduces a novel numerical approach to measure the bilinear condensate in 3D QCD using random matrix theory and eigenvalue analysis.

Findings

Confirmed the existence of a bilinear condensate in 3D QCD.

Estimated the condensate value as $oxed{rac{ ext{Sigma}}{ ext{lambda}^2} = 0.0042 \, ext{pm} \, 0.0004}$.

Demonstrated the effectiveness of a non-chiral random matrix model in extracting physical condensates.

Abstract

We find clear numerical evidence for a bilinear condensate in three-dimensional QCD in the 't Hooft limit. We use a non-chiral random matrix model to extract the value of the condensate $\Sigma$ from the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator. We estimate $\Sigma/\lambda^2 = 0.0042 \pm 0.0004$ in units of the physical 't Hooft coupling.