Chiral random matrix theory for two-color QCD at high density

TL;DR

This paper develops a non-Hermitian chiral random matrix theory for two-color QCD at high density, linking it to effective theories and spectral sum rules, and highlighting the BCS gap's role in the microscopic Dirac spectrum.

Contribution

It introduces a non-Hermitian chiral random matrix model that accurately describes two-color QCD at high density and connects it to effective theories and spectral properties.

Findings

Partition function matches the effective theory at high density.

Spectral sum rules are identical to those from the effective theory.

Microscopic Dirac spectrum is governed by the BCS gap.

Abstract

We identify a non-Hermitian chiral random matrix theory that corresponds to two-color QCD at high density. We show that the partition function of the random matrix theory coincides with the partition function of the finite-volume effective theory at high density, and that the Leutwyler-Smilga-type spectral sum rules of the random matrix theory are identical to those derived from the effective theory. The microscopic Dirac spectrum of the theory is governed by the BCS gap, rather than the conventional chiral condensate. We also show that with a different choice of a parameter the random matrix theory yields the effective partition function at low density.