(3+1)-Dimensional Topologically Massive 2-form Gauge Theory: Geometrical Superfield Approach

TL;DR

This paper develops a superfield formalism to derive complete off-shell nilpotent and anticommuting BRST and anti-BRST symmetries for a (3+1)D topologically massive non-Abelian 2-form gauge theory, revealing new CF-type conditions.

Contribution

It introduces a geometrical superfield approach with three horizontality conditions to systematically derive all BRST symmetries and associated CF-type conditions for the (3+1)D topologically massive gauge theory.

Findings

Derived full set of BRST and anti-BRST transformations.

Identified five CF-type conditions including two fermionic ones.

Demonstrated invariance of Lagrangians using superfield formalism.

Abstract

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations corresponding to the combined "scalar" and "vector" gauge symmetry transformations for the (3+1)-dimensional (4D) topologically massive non-Abelian $(B \wedge F)$ theory with the help of geometrical superfield formalism. For this purpose, we use three horizontality conditions (HCs). The first HC produces the (anti-)BRST transformations for the 1-form gauge field and corresponding (anti-)ghost fields whereas the second HC yields the (anti-)BRST transformations for 2-form field and associated (anti-)ghost fields. The integrability of second HC produces third HC. The latter HC produces the (anti-)BRST symmetry transformations for the compensating auxiliary vector field and corresponding ghosts. We obtain five (anti-)BRST invariant Curci-Ferrari (CF)-type conditions which emerge very naturally as the off-shoots of superfield formalism. Out of five CF-type conditions, two are fermionic in nature. These CF-type conditions play a decisive role in providing the absolute anticommutativity of the (anti-)BRST transformations and also responsible for the derivation of coupled but equivalent (anti-)BRST invariant Lagrangian densities. Furthermore, we capture the (anti-)BRST invariance of the coupled Lagrangian densities in terms of the superfields and translation generators along the Grassmannian directions $\theta$ and $\bar \theta$.