The General Supersymmetric Solution of Topologically Massive Supergravity

TL;DR

This paper derives the complete class of supersymmetric solutions in topologically massive supergravity, characterizing their geometric properties, boundary behavior, and associated charges, with implications for understanding supersymmetry and black hole solutions.

Contribution

It provides the first full classification of supersymmetric solutions in topologically massive supergravity, including their geometric structure and boundary conditions.

Findings

Solutions are of plane-wave type with a null Killing vector.

All solutions with a null Killing vector are supersymmetric for specific Chern-Simons couplings.

Critical coupling solutions exhibit logarithmic boundary singularities.

Abstract

We find the general fully non-linear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant \mu. If \mu does not take the critical value \mu=\pm 1, these solutions are asymptotically regular on a Poincar\'e patch, but do not admit a smooth global compactification with boundary S^1\times\R. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincar\'e patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole.