Massive 4D Abelian 2-form theory: Nilpotent symmetries from the (anti-)chiral superfield approach

Abstract

The off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetries are obtained by using the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism for the four [Formula: see text]-dimensional (4D) Stückelberg-modified massive Abelian 2-form gauge theory. We perform exactly similar kind of exercise for the derivation of the off-shell nilpotent (anti-)co-BRST symmetry transformations, too. In the above derivations, the symmetry invariant restrictions on the superfields play very important and decisive roles. To prove the sanctity of the above nilpotent symmetries, we generalize our 4D ordinary theory (defined on the 4D flat Minkowskian space–time manifold) to its counterparts [Formula: see text]-dimensional (anti-)chiral super-submanifolds of the [Formula: see text]-dimensional supermanifold which is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] [Formula: see text] are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] are fermionic: [Formula: see text], [Formula: see text] in nature. One of the novel observations of our present endeavor is the derivation of the Curci–Ferrari (CF)-type restrictions from the requirement of the symmetry invariance of the coupled (but equivalent) Lagrangian densities of our theory within the framework of ACSA to BRST formalism. We also exploit the standard techniques of ACSA to capture the off-shell nilpotency and absolute anticommutativity of the conserved (anti-)BRST as well as the conserved (anti-)co-BRST charges. In a subtle manner, the proof of the absolute anticommutativity of the above conserved charges also implies the existence of the appropriate CF-type restrictions on our theory. This proof is also a novel result.

Modified Stückelberg Formalism: Free Massive Abelian 2-Form Theory in 4D

“…First of all, the Lagrangian densities L (b 1 ) and L (b 2 ) have been derived in a completely different manner in our present endeavor if we compare our present method of derivation against the derivation in our earlier work [10], where we have exploited the method of trial and error. Second, the CF-type restrictions B + B + m φ = 0 and B + B + m φ = 0 are the same as in our earlier work [10,21], but the other two restrictions in (47) are different. Third, if we stick with the CF-type restrictions that have been derived from the superfield approach to BRST formalism in the context of 4D Abelian 2-form massless and massive gauge theories [18,21], we find that the other two restrictions of (47) are:…”

“…Second, the CF-type restrictions B + B + m φ = 0 and B + B + m φ = 0 are the same as in our earlier work [10,21], but the other two restrictions in (47) are different. Third, if we stick with the CF-type restrictions that have been derived from the superfield approach to BRST formalism in the context of 4D Abelian 2-form massless and massive gauge theories [18,21], we find that the other two restrictions of (47) are:…”

“…which are nothing but the (anti-)BRST and (anti-)co-BRST invariant CF-type restrictions on our theory (see, e.g., [10,21] for details).…”

“…Under the above discrete duality symmetry transformations, the coupled Lagrangian densities L (b 1 ) and L (b 2 ) are found to remain invariant even with the fixed choice of signs for the (pseudo-)scalar fields φ and φ. Finally, in the next section, we shall take only the simplest choices of the signs for the (pseudo-)scalar fields within the framework of BRST formalism where the Lagrangian density L (b 1 ) will be generalized to incorporate into it the Faddeev-Popov ghost terms by following the standard technique [10,18,21].…”

BRST and Related Superfield Approach to 1D and 2D Diffeomorphism Invariant Models of Particles and a Bosonic String: A Brief Review

“…Second, the (anti-)chiral supervariable approach (ACSA) to BRST formalism (see, e.g. [34][35][36] and references therein) has been exploited for the derivations of the (anti-) BRST symmetries for the rest of the variables of the theory in our earlier works [21][22][23][24][25] besides the phase variables (x µ , p µ ) for which the MBTSA has been exploited. Third, the standard (anti-)BRST symmetry transformations: s b C = i B, s b B = 0, s ab C = i B, s ab B = 0 have been taken into account in our present endeavor and earliear works [21][22][23][24][25] without any precise derivation.…”