Generalized Faddeev-Popov Method for a Deformed Supersymmetric Yang-Mills Theory

TL;DR

This paper extends the Faddeev-Popov method to deformed three-dimensional supersymmetric Yang-Mills theories with non-anticommutativity, addressing gauge fixing issues and exploring BRST symmetry in the context of supersymmetry breaking.

Contribution

It introduces a generalized Faddeev-Popov formalism for deformed supersymmetric gauge theories with non-anticommutativity, connecting to Nicolai maps and extended BRST symmetry.

Findings

Generalized Faddeev-Popov method for deformed theories

Analysis of gauge fixing in non-anticommutative supersymmetry

Study of extended BRST symmetry in the deformed setting

Abstract

In this paper, we will study the deformation of a three dimensional $\mathcal{N} = 2$ supersymmetry gauge theory. We will deform this theory by imposing non-anticommutativity. This will break the supersymmetry of the theory from $\mathcal{N} = 2$ supersymmetry to $\mathcal{N} = 1$ supersymmetry. We will address the problem that occurs in the Landau gauge due to the existence of multiple solutions to the gauge fixing condition. This will be done by generalizing the Faddeev-Popov method. This formalism is motivated from the Nicolai map in topological field theories. Finally, we will study the extended BRST symmetry that occurs in this theory.