Geometry and off-shell nilpotency for N = 1 supersymmetric Yang-Mills theory

TL;DR

This paper develops an off-shell nilpotent BRST and anti-BRST algebra for N=1 supersymmetric Yang-Mills theory using a superfield formalism, enabling a systematic construction of the quantum action.

Contribution

It introduces a superfield-based formalism to achieve off-shell nilpotency in supersymmetric Yang-Mills theory, extending the algebraic structure of gauge fixing.

Findings

Constructed off-shell nilpotent BRST and anti-BRST algebra

Derived gauge-fixed superaction from superfield formalism

Demonstrated consistency with supersymmetric gauge theories

Abstract

We show that for N = 1 supersymmetric Yang-Mills theory it is possible to build an off-shell nilpotent BRST and anti-BRST algebra in terms of a BRST superspace formalism. This is based on the introduction of the basic fields of the quantized theory together with an auxiliary real field via the lowest components of the superfield components of a superYang-Mills connection. Here, the associated supercurvature is constrained by horizontality conditions as in ordinary Yang-Mills theory. We also show how the off-shell BRST-invariant quantum action can be constructed starting from a gauge-fixed superaction.