On the Microscopic Spectra of the Massive Dirac Operator for Chiral Orthogonal and Chiral Symplectic Ensembles

TL;DR

This paper uses Random Matrix Theory to compute microscopic spectral correlators of the Euclidean Dirac operator for chiral orthogonal and symplectic ensembles, extending previous results to more general cases with arbitrary flavors, masses, and topological charge.

Contribution

It provides new closed-form formulas for spectral correlators of the Dirac operator in chiral orthogonal and symplectic ensembles with arbitrary parameters, using Widom's method.

Findings

Derived explicit formulas for spectral correlators in chOE and chSE

Extended previous QCD spectral results to general cases with multiple flavors and masses

Validated formulas through comparison with known special cases

Abstract

Using Random Matrix Theory we set out to compute the microscopic correlators of the Euclidean Dirac operator in four dimensions. In particular we consider: the chiral Orthogonal Ensemble (chOE), corresponding to a Yang-Mills theory with two colors and fermions in the fundamental representation, and the chiral Symplectic Ensemble (chSE), corresponding to any number of colors and fermions in the adjoint representation. In both cases we deal with an arbitrary number of massive fermions. We use a recent method proposed by H. Widom for deriving closed formulas for the scalar kernels from which all spectral correlation functions of the chGOE and chGSE can be determined. Moreover, we obtain complete analytic expressions of such correlators in the double microscopic limit, extending previously known results of four-dimensional QCD at beta=1 and beta=4 to the general case with N_f flavors, with arbitrary quark masses and arbitrary topological charge.