The Variational Field Equations of Cosmological Topologically Massive Supergravity

TL;DR

This paper formulates the equations of cosmological topologically massive supergravity in three dimensions, demonstrating local supersymmetry and deriving coupled field equations using a first order variational approach.

Contribution

It provides a complete set of coupled bosonic and fermionic field equations for the supergravity theory using a first order formalism with torsion constraints.

Findings

Explicit demonstration of local supersymmetry in the action density.

Derivation of complete coupled field equations in first order formalism.

Comparison with previous second order formalism results.

Abstract

We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three-dimensional Riemann-Cartan space-times. We use the language of exterior differential forms and the properties of Majorana spinors on 3-dimensional space-times to explicitly demonstrate the local supersymmetry of the action density involved. Coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion-constraint imposed by the method of Lagrange multipliers. We compare these field equations with the partial results given in the literature using a second order variational formalism.