Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations

Understand

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 U(1) 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.