A note on the (anti-)BRST invariant Lagrangian densities for the free abelian 2-form gauge theory

TL;DR

This paper demonstrates that the BRST and anti-BRST symmetry transformations for a free Abelian 2-form gauge theory are valid without explicitly imposing a specific constrained field condition, which naturally emerges from the equations of motion.

Contribution

It introduces coupled Lagrangian densities that are more elegant and economical, showing the emergence of the Curci-Ferrari type restriction from the equations of motion.

Findings

BRST and anti-BRST transformations are symmetry transformations of the Lagrangian densities.

The Curci-Ferrari type restriction emerges from the equations of motion.

The proposed Lagrangian densities are more aesthetically appealing and economical.

Abstract

We show that the previously known off-shell nilpotent (s_{(a)b}^2 = 0) and absolutely anticommuting (s_b s_{ab} + s_{ab} s_b = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (s_b) and anti-BRST transformations (s_{ab}) are the symmetry transformations of the appropriate Lagrangian densities of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s_{(a)b}. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.