Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory

Abstract

We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a toy model of the Hodge theory (i.e. a rigid rotor) and provide the geometrical meaning and interpretation to them. Furthermore, we also derive the nilpotent (anti-)co-BRST symmetry transformations for this theory within the framework of the above supervariable approach. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian of our present theory within the framework of augmented supervariable formalism. We also express the (anti-)BRST and (anti-)co-BRST charges in terms of the supervariables (obtained after the application of the (dual-)horizontality conditions and (anti-)BRST and (anti-)co-BRST invariant restrictions) to provide the geometrical interpretations for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing proper (i.e. nilpotent and absolutely anticommuting) fermionic (anti-)co-BRST symmetries are completely novel results in our present investigation.

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References in corpus (2)

• Self-Dual Chiral Boson: Augmented Superfield Approach
• The Hodge Operator Revisited

Cited by in corpus (5)

• Christ-Lee Model: (Anti-)Chiral Supervariable Approach to BRST Formalism
• BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor
• Nilpotent Charges of a Toy Model of Hodge Theory and an $\mathcal{N}$ = $2$ SUSY Quantum Mechanical Model: (Anti-)Chiral Supervariable Approach
• General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System
• Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism