Complex Langevin method applied to the 2D $SU(2)$ Yang-Mills theory

Abstract

The complex Langevin method in conjunction with the gauge cooling is applied to the two-dimensional lattice $SU(2)$ Yang-Mills theory that is analytically solvable. We obtain strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.

Comments: 10 pages, 7 figures, the final version to appear in Physical Review D