Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

TL;DR

This paper develops a supersymmetric extension of the horizontality condition to derive nilpotent BRST and anti-BRST symmetries for a free spinning relativistic particle, ensuring their absolute anticommutativity and consistent Lagrangian formulation.

Contribution

It introduces a novel supersymmetric modification of the horizontality condition within the superfield approach for a spinning particle, deriving explicit (anti-)BRST symmetries and an invariant Curci-Ferrari restriction.

Findings

Derived off-shell nilpotent (anti-)BRST transformations.

Established a supersymmetric modification of the horizontality condition.

Formulated (anti-)BRST invariant coupled Lagrangians.

Abstract

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (\tau) and a pair of odd (fermionic) variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,\; \theta \bar\theta + \bar\theta \theta = 0) of the Grassmann algebra. One of the most important features of our present investigation is the derivation of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST symmetry transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system.