Eur. Phys. J. C (2007) 51: 169-177
https://doi.org/10.1140/epjc/s10052-007-0282-y

Regular Article - Theoretical Physics

An alternative to the horizontality condition in the superfield approach to BRST symmetries

¹ Centre of Advanced Studies, Physics Department, Banaras Hindu University, P.O. BHU-Varanasi, Varanasi, 221005, India
² Block-JD Sector-III, On leave of absence from S.N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata, 700098, West Bengal, India

^* e-mail: malik@bose.res.in

Received: 27 May 2006
Revised: 15 December 2006
Published online: 1 June 2007

Abstract

We provide an alternative to the gauge covariant horizontality condition, which is responsible for the derivation of the nilpotent (anti-) BRST symmetry transformations for the gauge and (anti-) ghost fields of a (3+1)-dimensional (4D) interacting 1-form non-Abelian gauge theory in the framework of the usual superfield approach to the Becchi–Rouet–Stora–Tyutin (BRST) formalism. The above covariant horizontality condition is replaced by a gauge invariant restriction on the (4,2)-dimensional supermanifold, parameterised by a set of four spacetime coordinates, x^μ(μ=0,1,2,3), and a pair of Grassmannian variables, θ and θ̄. The latter condition enables us to derive the nilpotent (anti-) BRST symmetry transformations for all the fields of an interacting 1-form 4D non-Abelian gauge theory in which there is an explicit coupling between the gauge field and the Dirac fields. The key differences and the striking similarities between the above two conditions are pointed out clearly.