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 symmetry. We review some new approaches to -symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that -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 -symmetric extension of a φ4 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.
Highlights
Determining the phase diagram of quantum chromodynamics (QCD), the theory of the strong force, is an important goal with broad implications for nuclear and particle physics, astrophysics, and cosmology
The QCD phase diagram is often described as a function of the quark chemical potential μ and the temperature T
Much effort has been directed towards the development of algorithms to circumvent the sign problem [2, 3], we do not yet have a clear picture of QCD phase structure at finite density from lattice simulations
Summary
Determining the phase diagram of quantum chromodynamics (QCD), the theory of the strong force, is an important goal with broad implications for nuclear and particle physics, astrophysics, and cosmology. We have developed a Euclidean path integral technique which recasts a broad class of PT -symmetric scalar field theories with complex actions into real forms.
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