Nonlinear realisation approach to topologically massive supergravity

Abstract

We develop a nonlinear realisation approach to topologically massive supergravity in three dimensions, with and without a cosmological term. It is a natural generalisation of a similar construction for ${\cal N}=1$ supergravity in four dimensions, which was recently proposed by one of us. At the heart of both formulations is the nonlinear realisation approach to gravity which was given by Volkov and Soroka fifty years ago in the context of spontaneously broken local supersymmetry. In our setting, the action for cosmological topologically massive supergravity is invariant under two different local supersymmetries. One of them acts on the Goldstino, while the other supersymmetry leaves the Goldstino invariant. The former can be used to gauge away the Goldstino, and then the resulting action coincides with that given in the literature.