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Nilpotent charges of a toy model of Hodge theory and an $𝒩 = 2$ SUSY quantum mechanical model: (Anti-)chiral supervariable approach

T. Bhanja

http://orcid.org/0000-0001-7070-1353

Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi 221 005, UP, India

E-mail Address: tapobroto.bhanja@gmail.com

Corresponding author.

On leave of absence from: Department of Physics, IIT Guwahati, Guwahati 781039, Assam, India.

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N. Srinivas

Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi 221 005, UP, India

E-mail Address: seenunamani@gmail.com

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R. P. Malik

Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi 221 005, UP, India

DST Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University, Varanasi 221 005, India

E-mail Address: rpmalik1995@gmail.com

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https://doi.org/10.1142/S0217751X19501835Cited by:3 (Source: Crossref)

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 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 parametrized by the superspace coordinates $(t, 𝜃, \bar{𝜃})$ , where $t$ is the bosonic evolution parameter and $(𝜃, \bar{𝜃})$ are the Grassmannian variables which obey the standard fermionic relationships: $𝜃^{2} = {\bar{𝜃}}^{2} = 0$ , $𝜃 \bar{𝜃} + \bar{𝜃} 𝜃 = 0$ . 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 novel and surprising observation in our present endeavor where we have considered only the (anti-)chiral supervariables. To corroborate the novelty of the above observation, we apply this ACSA to an $𝒩 = 2$ SUSY quantum mechanical (QM) system of a free particle and show that the $𝒩 = 2$ SUSY conserved and nilpotent charges do not absolutely anticommute.

Keywords:

PACS: 11.15.-q, 03.70.+k, 11.30.-j, 11.30.Pb, 11.30.Qc

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