Novel 3D supersymmetric massive Yang-Mills theory

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.