$\mathcal PT$ symmetry, pattern formation, and finite-density QCD

TL;DR

This paper explores how $\, ext{PT}$-symmetric field theories can shed light on the complex phase structure of finite-density QCD, revealing stable patterned phases and offering new analytical and simulation approaches.

Contribution

It introduces new methods for analyzing $\, ext{PT}$-symmetric field theories and demonstrates their application to understanding phase patterns in finite-density QCD.

Findings

$\, ext{PT}$-symmetric theories have richer phase structures than Hermitian ones.

A $\, ext{PT}$-symmetric extension of $\, ext{phi}^4$ model shows patterned phases.

Finite density QCD models exhibit stable patterned phases in critical regions.

Abstract

A longstanding issue in the study of quantum chromodynamics (QCD) is its behavior at nonzero baryon density, which has implications for many areas of physics. The path integral has a complex integrand when the quark chemical potential is nonzero and therefore has a sign problem, but it also has a generalized $\mathcal PT$ symmetry. We review some new approaches to $\mathcal PT$-symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that $\mathcal PT$-symmetric field theories with more than one field generally have a much richer phase structure than their Hermitian counterparts, including stable phases with patterning behavior. The case of a $\mathcal PT$-symmetric extension of a $\phi^4$ model is explained in detail. The relevance of these results to finite density QCD is explained, and we show that a simple model of finite density QCD exhibits a patterned phase in its critical region.