Finite-density QCD, $\mathcal{P}\mathcal{T}$ symmetry, and dual algorithms

Abstract

Finite-density QCD and many other field theories with sign problems have a $\mathcal{P}\mathcal{T}$-type symmetry. After a brief introduction to $\mathcal{P}\mathcal{T}$-symmetric field theories, a real dual representation for $\mathcal{P}\mathcal{T}$-symmetric scalar field theories with complex actions is derived. We show that $\mathcal{P}\mathcal{T}$-symmetric field theories can exhibit exotic behavior, including sinusoidally modulated propagators, disorder lines, and spatially inhomogeneous pattern-forming phases. We discuss the interplay of duality, $\mathcal{P}\mathcal{T}$-symmetry and pattern formation using a ${\varphi }^4$ model and $Z(N)$ spin model with sign problems as examples. These behaviors may occur in finite-density QCD and related models.

9 pages, 1 figure. Proceedings of the 38th International Symposium on Lattice Field Theory, LATTICE2021, July 26-30, 2021