Augmented superfield approach to exact nilpotent symmetries for matter fields in non-Abelian theory

Abstract

We derive the nilpotent (anti-) BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3 + 1)-dimensional 1-form nonAbelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x µ (with µ = 0, 1, 2, 3) and a couple of Grassmannian variables θ and θ. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4, 1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed in the framework of augmented superfield formalism.

One-Form Abelian Gauge Theory as the Hodge Theory

“…In this attempt, however, the (anti-)BRST symmetry transformations associated with the matter fields of the gravitational theories have not yet been obtained. We can apply the theoretical arsenals of our newly proposed augmented superfield formulation [52,53,[57][58][59][60][61] to derive the nilpotent symmetry transformations associated with the matter fields. To derive the nilpotent (anti-)co-BRST symmetry transformations for the gravitational theory (in the framework of the superfield approach to BRST formalism) is yet another direction for further investigation.…”

“…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.…”

(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]). …”