Finite-density QCD, $\mathcal{PT}$ symmetry, and exotic phases

TL;DR

This paper explores the phase structure of finite-density QCD using analytic and lattice methods, revealing patterned ground states linked to $ ext{PT}$ symmetry and proposing a criterion for pattern formation.

Contribution

It introduces a novel approach applying $ ext{PT}$ symmetry concepts to finite-density QCD and derives a simple criterion for pattern formation in lattice models.

Findings

Patterned ground states near critical endpoints.

Application of $ ext{PT}$ symmetry to QCD models.

A criterion for pattern formation in lattice simulations.

Abstract

We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and $\mathcal{PT}$-symmetric QFTs. Finite-density QCD is symmetric under the combined operation of the charge and complex conjugation operators $\mathcal{CK}$, which falls into the class of so-called generalized $\mathcal{PT}$ symmetries. We show that $\mathcal{PT}$-symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy quark model at nonzero chemical potential that displays patterning behavior for a range of parameters. We derive a simple approximate criterion for the formation of these patterns, which can be used with lattice results.