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

TL;DR

This paper develops gauge-invariant off-shell formulations for massive 3D ${ m N}=2$ higher-spin supermultiplets using superspace reduction, extending previous massless models and constructing new supergravity counterparts.

Contribution

It introduces the first massive gauge-invariant 3D ${ m N}=2$ supersymmetric supergravity actions and extends off-shell formulations to massive higher-spin supermultiplets.

Findings

Derived off-shell actions for massive 3D ${ m N}=2$ supermultiplets via superspace reduction.

Constructed massive gauge-invariant 3D ${ m N}=2$ supergravity models.

Reduced models to ${ m N}=1$ superspace with consistent reality conditions.

Abstract

Making use of the known off-shell formulations for massless higher-spin ${\cal N}=1$ supermultiplets in four dimensions, gauge-invariant off-shell actions for massive higher-spin ${\cal N}=2$ 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 ${\cal N}=2$ supersymmetric counterparts of the linearised actions for the old and new minimal supergravity theories. Our off-shell ${\cal N}=2$ supermultiplets carry a non-zero central charge, and are formulated in 3D ${\cal N}=2$ central charge superspace. The models can be reduced to 3D ${\cal N}=1$ 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.