The Third way to 3D Supersymmetric Massive Yang-Mills Theory

TL;DR

This paper constructs a novel three-dimensional $ =1$ supersymmetric massive Yang-Mills theory that is consistent in a 'third way', not derived from a traditional action but still maintaining gauge invariance on-shell.

Contribution

It introduces the first off-shell supersymmetric massive YM model in 3D that is 'third way' consistent, expanding the understanding of non-standard gauge theories.

Findings

Successfully constructs the 3D $ =1$ supersymmetric massive YM theory.

Demonstrates the 'third way' consistency without a local action.

Shows the modified equations preserve gauge invariance on-shell.

Abstract

We construct three-dimensional, $\mathcal{N}=1$ 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 the modified YM equation, whose bosonic part coincides with the third way consistent pure massive YM model.