Nilpotent Charges of a Toy Model of Hodge Theory and an $\mathcal{N}$ = $2$ SUSY Quantum Mechanical Model: (Anti-)Chiral Supervariable Approach

Abstract

We derive the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for the system of a toy model of Hodge theory (i.e. a rigid rotor) by exploiting the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral supervariables that are defined on the appropriately chosen (1, 1)-dimensional super-submanifolds of the {\it general} (1, 2)-dimensional supermanifold on which our system of a one (0 + 1)-dimensional (1D) toy model of Hodge theory is considered within the framework of the augmented version of the (anti-)chiral supervariable approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism. The general (1, 2)-dimensional supermanifold is parameterized by the superspace coordinates ($t,\theta ,\bar{\theta }$) where $t$ is the bosonic evolution parameter and ($\theta ,\bar{\theta }$) are the Grassmannian variables which obey the standard fermionic relationships: ${\theta }^2={\bar{\theta }}^2=0,\theta \bar{\theta }+\bar{\theta }\theta =0$. We provide the geometrical interpretations for the symmetry invariance and nilpotency property. Furthermore, in our present endeavor, we establish the property of absolute anticommutativity of the conserved fermionic charges which is a completely {\it novel} and surprising observation in our present endeavor where we have considered {\it only} the (anti-)chiral supervariables. To corroborate the {\it novelty} of the above observation, we apply this ACSA to an $\mathcal{N}=2$ SUSY quantum mechanical (QM) system of a free particle and show that the $\mathcal{N}=2$ SUSY conserved and nilpotent charges do {\it not} absolutely anticommute.

LaTeX file, 21 pages, version to appear in IJMPA

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• Abelian 2-form gauge theory: superfield formalism
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• N = 2 SUSY symmetries for a moving charged particle under influence of a magnetic field: Supervariable approach
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Cited by in corpus (2)

• BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor
• Massive Spinning Relativistic Particle: Revisited Under BRST and Supervariable Approaches