Nilpotent Symmetries in Jackiw-Pi Model: Augmented Superfield Approach

TL;DR

This paper derives the complete set of off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetries for the (2+1)-dimensional Jackiw-Pi model using augmented superfield formalism, highlighting the role of CF conditions.

Contribution

It provides a novel derivation of (anti-)BRST transformations, including those of auxiliary fields, within the augmented superfield approach for the Jackiw-Pi model.

Findings

Derived complete off-shell nilpotent (anti-)BRST symmetries.

Identified CF-type conditions ensuring absolute anticommutativity.

Captured invariance of coupled Lagrangian densities in superfield formalism.

Abstract

We derive the complete set of off-shell nilpotent (s^2_{(a)b} = 0) and absolutely anticommuting (s_b s_{ab} + s_{ab} s_b = 0) Becchi-Rouet-Stora-Tyutin (BRST) (s_b) as well as anti-BRST symmetry transformations (s_{ab}) corresponding to the combined Yang-Mills and non-Yang-Mills symmetries of the (2 + 1)-dimensional Jackiw-Pi model within the framework of augmented superfield formalism. The absolute anticommutativity of the (anti-)BRST symmetries is ensured by the existence of two sets of Curci-Ferrari (CF) type of conditions which emerge naturally in this formalism. The presence of CF conditions enables us to derive the coupled but equivalent Lagrangian densities. We also capture the (anti-)BRST invariance of the coupled Lagrangian densities in the superfield formalism. The derivation of the (anti-)BRST transformations of the auxiliary field \rho is one of the key findings which can neither be generated by the nilpotent (anti-)BRST charges nor by the requirements of the nilpotency and/or absolute anticommutativity of the (anti-)BRST transformations. Finally, we provide a bird's-eye view on the role of auxiliary field for various massive models and point out few striking similarities and some glaring differences among them.