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

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).

LaTeX file, 28 pages, journal reference is given

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• Massive 4D Abelian 2-Form Theory: Nilpotent Symmetries from the (Anti-)Chiral Superfield Approach
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• Quantum Symmetries and Conserved Charges of the Cosmological Friedmann-Robertson-Walker Model
• Nilpotent Charges in an Interacting Gauge Theory and an N = 2 SUSY Quantum Mechanical Model: (Anti-)Chiral Superfield Approach
• Nilpotent Charges of a Toy Model of Hodge Theory and an $\mathcal{N}$ = $2$ SUSY Quantum Mechanical Model: (Anti-)Chiral Supervariable Approach
• 3D Jackiw-Pi Model: (Anti-)Chiral Superfield Approach to BRST Formalism
• BRST and Related Superfield Approach to a Few Interesting Models of Point Particles and a Model of Bosonic String: A Brief Review