Nilpotent Symmetries For Matter Fields In Non-Abelian Gauge Theory: Augmented Superfield Formalism

TL;DR

This paper derives off-shell nilpotent (anti-)BRST symmetries for matter fields in non-Abelian gauge theories using an augmented superfield approach on a (4+2)-dimensional supermanifold, addressing a longstanding problem.

Contribution

It introduces a novel augmented superfield formalism to derive (anti-)BRST symmetries for matter fields in arbitrary interacting gauge theories.

Findings

Derived nilpotent (anti-)BRST symmetries for Dirac matter fields.

Extended superfield approach to non-Abelian gauge theories.

Unified treatment of matter and gauge fields in BRST formalism.

Abstract

In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the (anti-)BRST nilpotent symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields $(\psi, \bar\psi)$ are derived in the framework of the augmented superfield formulation where the four $(3 + 1)$-dimensional (4D) interacting non-Abelian gauge theory is considered on the six $(4 + 2)$-dimensional supermanifold parametrized by the four even spacetime coordinates $x^\mu$ and a couple of odd elements ($\theta$ and $\bar\theta$) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge- and the (anti-)ghost fields of the theory in the general scheme of the augmented superfield formalism.