Abelian 2-form gauge theory: superfield formalism

TL;DR

This paper derives off-shell nilpotent BRST and anti-BRST symmetry transformations for a free Abelian 2-form gauge theory using a superfield approach, revealing a Curci-Ferrari type restriction that ensures their absolute anticommutativity.

Contribution

It introduces a superfield formalism to obtain BRST symmetries for Abelian 2-form gauge theory, highlighting the emergence of a Curci-Ferrari restriction and its relation to non-Abelian gauge theories.

Findings

BRST and anti-BRST transformations derived for all fields

Presence of a Curci-Ferrari type restriction ensuring anticommutativity

Insights into similarities between Abelian 2-form and non-Abelian gauge theories

Abstract

We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for {\it all} the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to BRST formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta \bar\theta + \bar\theta \theta = 0). One of the salient features of our present investigation is that the above nilpotent (anti-)BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well-known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our supperfield approach to the case of Abelian 3-form gauge theory in four (3 + 1)-dimensions of spacetime.