Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-09-11
Nucl.Phys. B702 (2004) 3-36
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, no figures, some references are added
Scientific paper
10.1016/j.nuclphysb.2004.08.032
In the previous works, we proposed the stochastic quantization method (SQM) approach to N=1 supersymmetric Yang-Mills theory (SSYM). 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 SSYM_4 in the superfield formalism. In this note, we apply the background field methd to SSYM_4 in terms of the stochastic action principle in SQM approach. The one-loop $\beta$-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 stochastic effective action in the background field method to the standard one in SQM.
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