Background Field Method in Stochastic Quantization of N = 1 Supersymmetric Yang-Mills Theory

TL;DR

This paper applies the background field method to N=1 supersymmetric Yang-Mills theory within stochastic quantization, confirming the method's consistency with known results and ghost contributions at the one-loop level.

Contribution

It introduces the background field approach into stochastic quantization of SSYM and verifies its agreement with traditional path-integral results at one-loop.

Findings

One-loop beta function matches path-integral results.

Stochastic gauge fixing reproduces ghost contributions.

Stochastic effective action is equivalent to the standard one.

Abstract

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.