(3+1)-Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

R Kumar,Debmalya Mukhopadhyay

doi:10.1140/epjc/s10052-018-5933-7

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 }.

Highlights

Symmetry is to provide the unitarity in various interactions under consideration [6]
Formalism, that the 4D free Abelian 2-form gauge theory provides a tractable field-theoretic model for Hodge theory where de Rham cohomological operators of differential geometry and Hodge duality operation find their physical realizations in terms of the continuous and discrete symmetries, respectively [36]
We focus on the derivation of the BRST and anti-BRST transformations for Bμν and correspondingghost fields

Summary

Introduction

The antisymmetric Kalb–Ramond field Bμν(= −Bνμ) of rank two became quite popular because of its relevance in the context of (super-)string theories [30,31], (super-)gravity theories [32], dual description of a massless scalar field [33,34] and noncommutative theories [35] It has been shown, within the framework of BRST formalism, that the 4D free Abelian 2-form gauge theory provides a tractable field-theoretic model for Hodge theory where de Rham cohomological operators of differential geometry and Hodge duality operation find their physical realizations in terms of the continuous and discrete symmetries, respectively [36]. The (anti-)BRST invariance of the coupled Lagrangian densities is shown in Appendix C

Geometrical significance of BRST symmetries: mathematical aspects

Coupled but equivalent Lagrangian densities

Conclusions