PT Symmetry and QCD: Finite Temperature and Density

TL;DR

This paper investigates the application of PT symmetry to quantum chromodynamics (QCD) at finite temperature and density, addressing key issues like the sign problem and confinement through PT-symmetric models and gauge theories involving monopoles.

Contribution

It demonstrates PT symmetry in effective actions for heavy quarks, solves the sign problem in a 1+1D model, and links PT-symmetric models to confinement mechanisms via monopole gases and affine Toda theories.

Findings

PT-symmetric Hamiltonian has real eigenvalues for certain chemical potentials

Effective theories for monopoles lead to sine-law string tension scaling

PT symmetry offers a potential solution to the QCD sign problem

Abstract

The relevance of PT symmetry to quantum chromodynamics (QCD), the gauge theory of the strong interactions, is explored in the context of finite temperature and density. Two significant problems in QCD are studied: the sign problem of finite-density QCD, and the problem of confinement. It is proven that the effective action for heavy quarks at finite density is PT-symmetric. For the case of 1+1 dimensions, the PT-symmetric Hamiltonian, although not Hermitian, has real eigenvalues for a range of values of the chemical potential $\mu$, solving the sign problem for this model. The effective action for heavy quarks is part of a potentially large class of generalized sine-Gordon models which are non-Hermitian but are PT-symmetric. Generalized sine-Gordon models also occur naturally in gauge theories in which magnetic monopoles lead to confinement. We explore gauge theories where monopoles cause confinement at arbitrarily high temperatures. Several different classes of monopole gases exist, with each class leading to different string tension scaling laws. For one class of monopole gas models, the PT-symmetric affine Toda field theory emerges naturally as the effective theory. This in turn leads to sine-law scaling for string tensions, a behavior consistent with lattice simulations.