Taming complex Langevin simulations of real-time lattice gauge theory with an anisotropic kernel

Abstract

The numerical computation of real-time observables in quantum field theories is a longstanding challenge, largely due to the infamous sign problem. While complex Langevin (CL) has emerged as a promising method to address this issue, its stability and convergence properties are problematic for certain physical systems. In this talk, I present our recent advances in applying CL to SU(2) lattice gauge theory in 3+1D on a complex Schwinger-Keldysh time contour. We studied the efficacy of stabilization methods such as gauge cooling and dynamical stabilization and found that they are insufficient to avoid wrong convergence in our simulations. To improve upon this, we propose a novel anisotropic kernel [1], which effectively stabilizes our simulations and leads to correct convergence of expectation values. These findings suggest that our method may enable us to calculate real-time observables including transport coefficients from first principles. [1] K. Boguslavski, P. Hotzy and D. I. Müller [arXiv:2212.08602 [hep-lat]]