Lifshitz-type gauge theory with 𝒩 = 2 supersymmetry

We construct an [Formula: see text] supersymmetric gauge theory in Lifshitz space–time. Starting with [Formula: see text] supersymmetric Lagrangian, we introduce an additional [Formula: see text] symmetry between specific component fields. The resultant Lagrangian is shown to have an extra set of supersymmetry, thus realizing an on-shell [Formula: see text] supersymmetric gauge theory. Just as in the case of [Formula: see text], the superderivatives and superfields involved contain higher-order derivatives of spatial coordinates. The constructed [Formula: see text] supersymmetric Lagrangian has both vector multiplet and hypermultiplet.