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

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 Becchi-Rouet-Stora-Tyutin (BRST) formalism. The above covariant horizontality condition is replaced by a gauge invariant restriction on the (4, 2)-dimensional supermanifold, parameterized by a set of four spacetime coordinates x µ (µ = 0, 1, 2, 3) and a pair of Grassmannian variables θ andθ. 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 where there is an explicit coupling between the gauge field and the Dirac fields. The key differences and striking similarities between the above two conditions are pointed out clearly.

One-Form Abelian Gauge Theory as the Hodge Theory

“…In the framework of the augmented superfield formulation, there are ways to derive the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for all the fields of the Lagrangian density (A.1) of the theory [52][53][54][55][56][57][58][59][60][61]. The long-standing problem of the derivation of the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for the matter fields ψ andψ of the interacting gauge theory, in the framework of the superfield approach to BRST formalism, has been resolved by taking recourse to (i) the equality of some conserved quantities [52,53,[57][58][59][60][61] on the appropriate dimensional supermanifold (e.g.…”

“…Exploiting the mappings given in (4.49), it can be seen that the symmetric energy-momentum tensor can also be written in the following total derivative forms 55) where the expansions for the superfields have to be inserted from (4.44) and (4.45) which have been obtained after the applications of HC and DHC. In the language of the geometry on the four (2, 2)-dimensional supermanifold, it can be seen that the symmetrical energy momentum tensor is equivalent to the translations (i) along the Grassmannianθ-direction of the supermanifold when a specific combination of the Lorentz scalar composite superfields (cf.…”

(Anti)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory

“…In other words, there are no (anti)chiral expansions for this field which implies that the superfield generalization is ( ) →̃( B, , , ) ( , ) = ( ). Here we have taken the results of earlier works [20,21,[25][26][27][28] where it has been established that the coefficients of and/or correspond to the nilpotent symmetries. In this context, it is pertinent to point out that the BRST invariant quantities (when generalized onto a (2, 1)-dimensional antichiral supersubmanifold) must be independent of the "soul" coordinate because the latter is not physically realized.…”

“…gauge theory. This has been systematically generalized so as to derive the proper (anti-)BRST symmetry transformations ( ( ) ) for the matter, gauge and (anti-)ghost fields together for a given interacting -form gauge theory (see, e.g., [25][26][27][28]). The latter superfield formalism exploits the additional restrictions (e.g., gauge invariant restrictions) which are found to be consistent with the celebrated HC.…”

“…The latter superfield formalism exploits the additional restrictions (e.g., gauge invariant restrictions) which are found to be consistent with the celebrated HC. These theoretical formulations have been christened as the augmented version of superfield formalism (see, e.g., [25][26][27][28]). …”