Abstract :
In the previous works, we proposed the stochastic quantization method (SQM) approach to image 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 image in the superfield formalism. In this note, we apply the background field method to image 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 Zwanzigerʹs 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.
