Eur. Phys. J. C (2018) 78: 452
https://doi.org/10.1140/epjc/s10052-018-5933-7

Regular Article - Theoretical Physics

-Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

¹ Department of Physics and Astrophysics, University of Delhi, New Delhi, 110007, India
² Department of Theoretical Physics, Indian Association for the Cultivation of Science, 2A and B Raja S.C. Mullick Road, Jadavpur, Kolkata, 700032, India
³ Present address: Variable Energy Cyclotron Centre (VECC), 1/AF, Bidhannagar, Kolkata, West Bengal, 700064, India

^* e-mail: raviphynuc@gmail.com

Received: 17 October 2017
Accepted: 27 May 2018
Published online: 5 June 2018

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 -dimensional (4D) topologically massive non-Abelian 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 and .