Three-dimensional N=2 supergravity theories: From superspace to components

TL;DR

Three-dimensional $\mathcal{N}=2$ supergravity theories are developed by reducing off-shell superspace actions to components and unifying Type I/II minimal, non-minimal, and topologically massive formulations, with a universal background construction for supersymmetric curved spaces. A closed super three-form method yields locally supersymmetric and super-Weyl invariant actions, from which explicit Type I and II minimal, as well as topologically massive, component actions are derived; various gauge choices connect conformal supergravity to Poincaré and AdS theories. The paper further analyzes the symmetry structure of curved $\mathcal{N}=2$ superspace, classifies backgrounds with different numbers of preserved supercharges, and provides a framework for constructing rigid supersymmetric theories on curved 3D backgrounds, including AdS and four-supercharge configurations. Overall, the work supplies a practical toolkit for building 3D $\mathcal{N}=2$ supergravity–matter systems and for exploring rigid supersymmetry on curved 3D geometries via compensators and gauge choices.

Abstract

For general off-shell N=2 supergravity-matter systems in three spacetime dimensions, a formalism is developed to reduce the corresponding actions from superspace to components. The component actions are explicitly computed in the cases of Type I and Type II minimal supergravity formulations. We describe the models for topologically massive supergravity which correspond to all the known off-shell formulations for three-dimensional N=2 supergravity. We also present a universal setting to construct supersymmetric backgrounds associated with these off-shell supergravities.