Three-dimensional supergravity reloaded

TL;DR

This paper constructs a three-dimensional supergravity theory incorporating a variety of geometric terms, demonstrating its formulation as a Chern-Simons theory for supersymmetric Poincare and AdS groups, and extends it to multiple gravitini.

Contribution

It provides a comprehensive supersymmetric extension of the most general 3D gravity theory, including torsion and Chern-Simons formulations, with extensions to multiple gravitini.

Findings

Supergravity action expressed as a Chern-Simons theory for supersymmetric groups.

Inclusion of torsion and Lorentz-Chern-Simons terms with arbitrary couplings.

Extension to N = p+q gravitini cases.

Abstract

The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with cosmological constant, the gravitational sector contains the Lorentz-Chern-Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern-Simons theory for the supersymmetric extension of the Poincare and AdS groups, respectively. The construction can be simply carried out by making use of a duality map between different gravity theories discussed here, which relies on the different ways to make geometry emerge from a single gauge potential. The extension for N =p+q gravitini is also performed.