Nilpotent Charges in an Interacting Gauge Theory and an N = 2 SUSY Quantum Mechanical Model: (Anti-)Chiral Superfield Approach

TL;DR

This paper uses the (anti-)chiral superfield approach to derive nilpotent (anti-)BRST symmetries and charges in interacting non-Abelian gauge theories and demonstrates their properties, also applying the method to an N=2 SUSY quantum mechanical model.

Contribution

It introduces a novel application of the (anti-)chiral superfield approach to establish absolute anticommutativity of BRST charges in non-Abelian gauge theories and explores its implications in SUSY quantum mechanics.

Findings

Derived nilpotent (anti-)BRST symmetries for non-Abelian gauge theories.

Proved absolute anticommutativity of BRST charges using ACSA.

Showed non-anticommutativity of supercharges in N=2 SUSY QM.

Abstract

We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the nilpotent (anti-)BRST symmetry transformations for any arbitrary D-dimensional interacting non-Abelian 1-form gauge theory where there is a SU(N) gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our present endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the (D, 1)-dimensional super-submanifolds of the general (D, 2)-dimensional supermanifold on which our D-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. To corroborate the novelty of the above result, we apply the ACSA to an N = 2 supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic oscillator and show that the nilpotent and conserved N = 2 supercharges of this system do not absolutely anticommute.