Spectra of massive and massless QCD Dirac operators: A novel link

TL;DR

This paper uncovers a new connection between the spectral statistics of massive and massless QCD Dirac operators using integrable structures in random matrix models, and validates the universality of these statistics with lattice data.

Contribution

It establishes a novel link between spectral statistics of massive and massless QCD Dirac operators through integrable random matrix models, and proves universality for specific cases.

Findings

Derived explicit spectral statistics for SU(2) massive fermions.

Proved universality of low-lying eigenvalue statistics.

Confirmed theoretical predictions with lattice data.

Abstract

We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta=1,2, and 4) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for beta-fold degenerate massive fermions is used to explicitly derive (and prove the random matrix universality of) statistics of low--lying eigenvalues of QCD Dirac operators in the presence of SU(2) massive fermions in the fundamental representation (beta=1) and SU(N_c >= 2) massive adjoint fermions (beta=4). Comparison with available lattice data for SU(2) dynamical staggered fermions reveals a good agreement.