Cluster expansions and chiral symmetry at large density in 2-color QCD

TL;DR

This paper uses cluster expansions to analyze chiral symmetry in 2-color QCD at high density, revealing that certain lattice artifacts prevent the expected superfluidity and superconductivity phases.

Contribution

It extends cluster expansion techniques to finite density lattice gauge theories with real fermion determinants, demonstrating chiral symmetry behavior at any coupling.

Findings

Cluster expansions converge at high density for theories with real determinants.

Absence of color superfluidity/superconductivity is identified as a lattice artifact.

Discussion of potential methods to overcome lattice saturation issues.

Abstract

$SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions are considered at high quark chemical potential $\mu$ and any temperature $T$. In the strong coupling regime (sufficiently small $\beta$) they have been shown to possess a chiral phase of intact global $U(N_f)\times U(N_f)$ symmetry. The proof is by cluster expansions which converge in the infinite volume limit. Extension to weaker coupling does not appear feasible in the presence of complex fermion determinant. For theories with real determinant, however, such as 2-color QCD with fundamental fermions, or any $N_c$ with even $N_f$ and adjoint fermions, such large $\mu$ cluster expansions can be used to show chiral behavior of fermionic lattice observables at any gauge coupling. Unfortunately, this absence of color superfluidity/superconductivity at high $\mu$ appears to be a lattice artifact due to lattice saturation, a serious problem plaguing the standard finite density formalism on the lattice. Some possible ways of circumventing saturation are discussed.