$\mathcal{P}T$ symmetry, pattern formation, and finite-density QCD

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 $\mathcal{P}T$ symmetry. We review some new approaches to $\mathcal{P}T$-symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that $\mathcal{P}T$-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 $\mathcal{P}T$-symmetric extension of a ${\varphi }^4$ 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.

arXiv comment25 pages, 8 figures. To be published in Journal of Physics: Conference Series as part of the virtual seminar series on Pseudo-Hermitian Hamiltonians in Quantum Physics (vPHHQP)

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• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Dilepton production from moaton quasiparticles
• Revisiting the spatially inhomogeneous condensates in the $(1+1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit
• Dissecting the moat regime at low energies I: Renormalization and the phase structure