Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter Fields In Non-Abelian Theory

TL;DR

This paper develops a superfield formalism to derive exact nilpotent BRST symmetry transformations for matter fields in a non-Abelian gauge theory, providing geometric insights and extending previous approaches.

Contribution

It introduces an augmented superfield approach combining horizontality and gauge invariance to obtain both on-shell and off-shell BRST symmetries for matter fields in non-Abelian theories.

Findings

Derived on-shell nilpotent BRST transformations for matter fields.

Obtained off-shell nilpotent BRST transformations using full supermanifold.

Provided geometric interpretation of the symmetry transformations.

Abstract

We derive the nilpotent (anti-)BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x^\mu (with \mu = 0,1,2,3) and a couple of Grassmannian variables \theta and \bar{\theta}. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4, 1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed in the framework of augmented superfield formalism.