The Variational Field Equations of Cosmological Topologically Massive Supergravity

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. Exact 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. Cotton and Cottino 2-forms that are complete to all orders in the gravitino field are derived and their properties such as trace are investigated.

Automated summary

In this article, the formulation of cosmological topologically massive supergravity theory in three-dimensional Riemann-Cartan space-times is discussed using the language of exterior differential forms and Majorana spinors. The local supersymmetry of the action density is explicitly demonstrated, and exact coupled field equations are derived by a first order variational principle subject to a torsion-constraint imposed by Lagrange multipliers. Cotton and Cottino 2-forms complete to all orders in the gravitino field are derived and their properties are investigated.