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Novel 3D supersymmetric massive Yang-Mills theory

Nihat Sadik Deger ^1,* and Jan Rosseel^2,†

¹Department of Mathematics, Bogazici University, Bebek, 34342 Istanbul, Turkey
²Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

^*sadik.deger@boun.edu.tr
^†jan.rosseel@univie.ac.at

Phys. Rev. D 104, L081701 – Published 1 October, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L081701

Abstract

We construct three-dimensional, $N = 1$ off-shell supersymmetric massive Yang-Mills (YM) theory whose YM equation is “third-way” consistent. This means that the field equations of this model do not come from variation of a local action without additional fields, yet the gauge-covariant divergence of the YM equation still vanishes on shell. To achieve this, we modify the massive Majorana spinor equation so that its supersymmetry variation gives a modified YM equation whose bosonic part coincides with the third-way consistent pure massive YM model.

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References (19)

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Our Clifford algebra and spinor conventions are as follows. The charge conjugation matrix $C$ obeys $γ_{μ}^{T} = - C γ_{μ} C^{- 1}$ , $C^{T} = - C$ . The following properties for bilinears involving Majorana spinors then hold: $\bar{χ} ε = \bar{ε} χ$ , $\bar{χ} γ^{μ} ε = - \bar{ε} γ^{μ} χ$ . The Fierz identity reads: $χ \bar{ε} = - \frac{1}{2} \bar{ε} χ 1 - \frac{1}{2} \bar{ε} γ^{μ} χ γ_{μ}$ . Some useful $γ$ -matrix relations are $γ^{ν} γ^{μ} γ_{ν} = - γ^{μ}$ , $γ^{μ ν} = ε^{μ ν ρ} γ_{ρ}$ , $γ_{μ} = - \frac{1}{2} ε_{μ ν ρ} γ^{ν ρ}$ , $γ^{μ ν ρ} = ε^{μ ν ρ} 1$ .
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We are grateful to Paul Townsend for making this suggestion.
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Phys. Rev. D 104, L081701– Published 1 October, 2021

Vol. 104, Iss. 8 — 15 October 2021

Received 10 June 2021
Accepted 31 August 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L081701

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Novel 3D supersymmetric massive Yang-Mills theory

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