Real-time lattice gauge theory actions: Unitarity, convergence, and path integral contour deformations
Gurtej Kanwar and Michael L. Wagman
Phys. Rev. D 104, 014513 (2021) - Published 30 July, 2021
The Wilson action for Euclidean lattice gauge theory defines a positive-definite transfer matrix that corresponds to a unitary lattice gauge theory time-evolution operator if analytically continued to real time. Hoshina, Fujii, and Kikukawa (HFK) recently pointed out that applying the Wilson action discretization to continuum real-time gauge theory does not lead to this, or any other, unitary theory and proposed an alternate real-time lattice gauge theory action that does result in a unitary real-time transfer matrix. The character expansion defining the HFK action is divergent, and in this work we apply a path integral contour deformation to obtain a convergent representation for HFK path integrals suitable for numerical Monte Carlo calculations. We also introduce a class of real-time lattice gauge theory actions based on analytic continuation of the Euclidean heat-kernel action. Similar divergent sums are involved in defining these actions, but for one action in this class this divergence takes a particularly simple form, allowing construction of a path integral contour deformation that provides absolutely convergent representations for and real-time lattice gauge theory path integrals. We perform proof-of-principle Monte Carlo calculations of real-time and lattice gauge theory and verify that exact results for unitary time evolution of static quark-antiquark pairs in ()D are reproduced.