Background field method in stochastic quantization of [formula omitted] supersymmetric Yang–Mills theory

Abstract

In the previous works, we proposed the stochastic quantization method (SQM) approach to N = 1 supersymmetric Yang–Mills theory (SYM). In four dimensions, in particular, we obtained the superfield Langevin equation and the corresponding Fokker–Planck equation which describe the underlying stochastic process manifestly preserving the global supersymmetry as well as the local gauge symmetry. The stochastic gauge fixing procedure was also applied to SYM 4 in the superfield formalism. In this note, we apply the background field method to SYM 4 in terms of the stochastic action principle in the SQM approach. The one-loop β-function for the gauge coupling agrees with that given by the path-integral approach, thereby confirming that the stochastic gauge fixing procedure with the background local gauge invariant Zwanziger's gauge fixing functions simulates the contributions from the Nielsen–Kallosh ghost as well as the Faddeev–Popov ghost at the one-loop level. We also show the equivalence of the effective stochastic action in the background field method to the standard one in SQM.