A stabilizing kernel for complex Langevin simulations of real-time gauge theories

TL;DR

This paper introduces a new anisotropic kernel for the complex Langevin method, enabling stable real-time gauge theory simulations on discretized contours, potentially allowing first-principles calculations of real-time observables.

Contribution

It develops a novel anisotropic kernel for complex Langevin simulations, improving stability in real-time gauge theories on Schwinger-Keldysh contours.

Findings

Achieved unprecedented stability in SU(2) Yang-Mills simulations.

Enabled potential first-principles calculations of real-time observables.

Revised discretization approach for complex Langevin equations.

Abstract

The complex Langevin (CL) method is a promising approach to overcome the sign problem, which emerges in real-time formulations of quantum field theories. Over the past decade, stabilization techniques for CL have been developed with important applications in finite density QCD. However, they are insufficient for SU($N_c$) gauge theories on a Schwinger-Keldysh time contour that is required for a real-time formulation. In these proceedings we revise the discretization of the real-time CL equations and introduce a novel anisotropic kernel that enables CL simulations on discretized time contours. Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that may allow us to calculate real-time observables from first principles.