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

Abstract

Finite-density QCD and many other field theories with sign problems have a PT -type symmetry. After a brief introduction to PT -symmetric field theories, a real dual representation for PTsymmetric scalar field theories with complex actions is derived. We show that PT -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, PT -symmetry and pattern formation using a 𝜙 4 model and 𝑍 (𝑁) spin model with sign problems as examples. These behaviors may occur in finite-density QCD and related models.