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

TL;DR

This paper uses the supervariable approach to derive and interpret nilpotent BRST and co-BRST symmetries for a toy model of Hodge theory, revealing their geometric meaning and novel dual-horizontality conditions.

Contribution

It introduces a novel application of the supervariable approach to derive (anti-)co-BRST symmetries and their geometric interpretation in a toy Hodge theory model.

Findings

Derived nilpotent BRST and anti-BRST transformations with geometric meaning.

Established nilpotent (anti-)co-BRST symmetries using dual-horizontality conditions.

Provided geometrical interpretation of symmetry charges and invariances.

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.