Eur. Phys. J. C (2009) 60: 457-470
https://doi.org/10.1140/epjc/s10052-009-0918-1

Regular Article - Theoretical Physics

Abelian 2-form gauge theory: superfield formalism

Centre of Advanced Studies, Physics Department, Banaras Hindu University, Varanasi, 221 005, UP, India

^* e-mail: malik@bhu.ac.in
^** e-mail: rudra.prakash@hotmail.com

Received: 30 September 2008
Revised: 27 November 2008
Published online: 19 February 2009

Abstract

We derive the off-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to the 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 ^μ (with μ=0,1,2,3) and a pair of odd Grassmannian variables θ and (with ). 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 superfield approach to the case of Abelian 3-form gauge theory in four, (3+1), dimensions of spacetime.