Gauge-invariant off-shell formulations for 3D massive higher-spin supermultiplets

A bstract Making use of the known off-shell formulations for massless higher-spin 𝒩 = 1 supermultiplets in four dimensions, gauge-invariant off-shell actions for massive higher-spin 𝒩 = 2 supermultiplets in three dimensions (3D) are derived by Kaluza-Klein reduction in superspace. To illustrate the formalism, we also construct, for the first time, massive gauge-invariant 3D 𝒩 = 2 supersymmetric counterparts of the linearised actions for the old and new minimal supergravity theories. Our off-shell 𝒩 = 2 supermultiplets carry a non-zero central charge, and are formulated in 3D 𝒩 = 2 central charge superspace. The models can be reduced to 3D 𝒩 = 1 superspace, by integrating out two Grassmann variables, and then consistent reality conditions on the superfields can be imposed. As a result, only two supercharges remain unbroken.