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3D Jackiw–Pi model: (anti-)chiral superfield approach to BRST formalism

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Abstract

We discuss and derive the continuous Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for the Jackiw–Pi (JP) model of three (2 + 1)-dimensional (3D) massive non-Abelian 1-form gauge theory by exploiting the standard technique of (anti-)chiral superfield approach (ACSA) to BRST formalism where a few appropriate and specific sets of (anti-)BRST invariant quantities (i.e., physical quantities at quantum level) play a very important role. We provide the explicit derivation of the nilpotency and absolute anticommutativity properties of (anti-)BRST conserved charges and existence of Curci–Ferrari (CF)-condition within the realm of ACSA to BRST formalism where we take only a single Grassmannian variable into account. We also provide the clear proof of (anti-)BRST invariances of the coupled (but equivalent) Lagrangian densities within the framework of ACSA to BRST approach where the emergence of the CF-condition is observed.

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Notes

  1. According to the Noether theorem whenever any Lagrangian density or its corresponding action remains invariant under any continuous symmetry transformations, there exits conserved currents and charges corresponding to that given continuous symmetries.

  2. We obtain the following expressions after the application of \(s_b\) on \({\mathcal {Q}}_{ab}\) and \(s_{ab}\) on \({\mathcal {Q}}_{b}\) for the proof of absolute anticommutativity as: \(s_b {\mathcal {Q}}_{ab} = -\, i\int d^2x \Big [\bar{{\mathcal {B}}} \cdot \partial ^0 \Big ({\mathcal {B}} + \bar{{\mathcal {B}}} \,+ \,i \, g\, (\bar{C}\times C)\Big )\Big ] = -\,i\,\{{\mathcal {Q}}_b, {\mathcal {Q}}_{ab}\} = 0\) and \(s_{ab} {\mathcal {Q}}_b = i \int d^2x \Big [{\mathcal {B}} \cdot \partial ^0 \Big ({\mathcal {B}} + \bar{{\mathcal {B}}} \,+ \,i \, g\, (\bar{C}\times C)\Big )\Big ] = -\,i\,\{{\mathcal {Q}}_{ab}, {\mathcal {Q}}_{b}\} = 0\).

  3. The (anti-)BRST invariant quantities are obtained using nilpotency property of (anti-)BRST symmetry transformations Eqs. (7) and (8) and some of them are determined by the hit and trial method.

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Acknowledgements

The present investigation has been carried out under the DST-INSPIRE fellowship (Govt. of India) awarded to the author. The author of this paper expresses their gratefulness to the above national funding agency as well as A. K. Rao for a careful reading of the manuscript. Fruitful and enlightening comments by our esteemed Reviewer are thankfully acknowledged.

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  1. Physics Department, Centre of Advance Studies, Institute of Science, Banaras Hindu University, Varanasi, UP, 221 005, India

    B. Chauhan

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Chauhan, B. 3D Jackiw–Pi model: (anti-)chiral superfield approach to BRST formalism. Eur. Phys. J. Plus 137, 976 (2022). https://doi.org/10.1140/epjp/s13360-022-03161-0

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