Topologically massive non-Abelian theory: superfield formalism

TL;DR

This paper applies superfield formalism to derive BRST symmetries and CF-type restrictions in a 4D non-Abelian 2-form gauge theory, providing a geometric understanding of gauge invariances and symmetry structures.

Contribution

It extends superfield approach to non-Abelian 2-form gauge theories, deriving off-shell nilpotent BRST symmetries and CF restrictions, and explores their algebraic properties.

Findings

Derived off-shell nilpotent BRST and anti-BRST transformations.

Established CF-type restrictions responsible for symmetry anticommutativity.

Constructed BRST-invariant coupled Lagrangian densities.

Abstract

We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3 + 1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-) BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-) BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-) BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-) BRST symmetry transformations when the (anti-) BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-) BRST symmetries are, however, found to be not absolutely anticommuting in nature.