Chiral Lagrangian and spectral sum rules for dense two-color QCD

TL;DR

This paper analytically explores the low-energy behavior and spectral properties of dense two-color QCD with many flavors, deriving exact partition function dependencies and spectral sum rules relevant for lattice tests.

Contribution

It introduces a new epsilon-regime at high density and derives spectral sum rules for the Dirac operator eigenvalues in dense two-color QCD.

Findings

Derived exact quark mass dependence of the partition function.

Established spectral sum rules for Dirac eigenvalues.

Proposed tests for lattice QCD simulations.

Abstract

We analytically study two-color QCD with an even number of flavors at high baryon density. This theory is free from the fermion sign problem. Chiral symmetry is broken spontaneously by the diquark condensate. Based on the symmetry breaking pattern we construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons. We identify a new epsilon-regime at high baryon density in which the quark mass dependence of the partition function can be determined exactly. We also derive Leutwyler-Smilga-type spectral sum rules for the complex eigenvalues of the Dirac operator in terms of the fermion gap. Our results can in principle be tested in lattice QCD simulations.