Nilpotent Symmetries of a 4D Model of the Hodge Theory: Augmented (Anti-)Chiral Superfield Formalism

TL;DR

This paper derives nilpotent BRST, anti-BRST, and (anti-)co-BRST symmetries for a 4D Abelian 2-form gauge theory using superfield formalism on (anti-)chiral supermanifolds, revealing novel symmetry properties.

Contribution

It introduces a new derivation of proper (anti-)co-BRST symmetries and proves their absolute anticommutativity using only (anti-)chiral superfields.

Findings

Derived nilpotent symmetries using superfield restrictions.

Proved absolute anticommutativity of conserved charges.

Presented novel results on (anti-)co-BRST symmetries.

Abstract

We derive the continuous nilpotent symmetries of the four (3 + 1)-dimensional (4D) model of the Hodge theory (i.e. 4D Abelian 2-form gauge theory) by exploiting the beauty and strength of the symmetry invariant restrictions on the (anti-)chiral superfields. The above off-shell nilpotent symmetries are the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST transformations which turn up beautifully due to the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral superfields that are defined on the (4, 1)-dimensional (anti-)chiral super-submanifolds of the general (4, 2)-dimensional supermanifold on which our ordinary 4D theory is generalized. The latter supermanifold is characterized by the superspace coordinates $Z^M = (x^\mu,\, \theta,\, \bar\theta)$ where $x^\mu\, (\mu = 0, 1, 2, 3 )$ are the bosonic coordinates and a pair of Grassmannian variables $\theta$ and $\bar\theta$ are fermionic in nature as they obey the standard relationships: $\theta^2 = {\bar\theta}^2 = 0,\, \theta\,\bar\theta + \bar\theta\,\theta = 0$). The derivation of the {\it proper} (anti-)co-BRST symmetries and proof of the absolute anticommutativity property of the conserved (anti-)BRST and (anti-) co-BRST charges are novel results of our present investigation (where only the (anti-)chiral superfields and their super-expansions have been taken into account).