Superfield approach to nilpotent symmetries in 3D Jackiw-Pi model of massive non-Abelian theory

TL;DR

This paper develops a superfield formalism to derive off-shell nilpotent and anticommuting (anti-)BRST symmetries for the 3D Jackiw-Pi non-Abelian gauge theory, including novel transformations for auxiliary fields.

Contribution

It introduces a superfield approach that unifies the derivation of (anti-)BRST symmetries and auxiliary field transformations in the 3D Jackiw-Pi model, extending previous methods.

Findings

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

Established the Curci-Ferrari restriction for this model.

Obtained novel (anti-)BRST transformations for auxiliary fields.

Abstract

In the available literature, only the Becchi-Rouet-Stora-Tyutin (BRST) symmetries are known for the Jackiw-Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent (s_{(a)b}^2 = 0) and absolutely anticommuting (s_b \,s_{ab} + s_{ab}\, s_b = 0) (anti-)BRST transformations s_{(a)b} corresponding to the usual Yang-Mills gauge transformations of this model by exploiting the "augmented" superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang-Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci-Ferrari restriction which plays a key role in the proof of absolute anticommutativity of s_{(a)b}. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field \rho from our superfield formalism which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and/or absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.