Supersymmetric solutions of N=(1,1) general massive supergravity

N S Deger,Ö Sarıoğlu,Z Nazari

doi:10.1103/physrevd.97.106022

Abstract

We construct supersymmetric solutions of three dimensional N = (1,1) General Massive Supergravity (GMG). Solutions with a null Killing vector are in general pp-waves. We identify those that appear at critical points of the model some of which do not exist in N = (1,1) New Massive Supergravity (NMG). In the timelike case, we find that many solutions are common with NMG but there is a new class that is genuine to GMG, two members of which are stationary Lifshitz and timelike squashed AdS spacetimes. We also show that in addition to the fully supersymmetric AdS vacuum, there is a second AdS background with a non-zero vector field that preserves 1/4 supersymmetry.

Highlights

Trying to understand quantum gravity in threedimensional rather than four-dimensional spacetime is a technically more manageable problem
Solutions with a null Killing vector are, in general, pp-waves. We identify those that appear at critical points of the model, some of which do not exist in N 1⁄4 ð1; 1Þ new massive supergravity (NMG)
We find that many solutions are common with NMG, but there is a new class that is genuine to general massive gravity (GMG), two members of which are stationary Lifshitz and timelike squashed anti-de Sitter (AdS) spacetimes

Summary

INTRODUCTION

Trying to understand quantum gravity in threedimensional rather than four-dimensional spacetime is a technically more manageable problem. A reason for this is that a three-dimensional gravity theory on anti-de Sitter (AdS) space is dual to a two-dimensional conformal field theory (CFT), and such CFTs are much better understood compared to higher-dimensional ones With this goal in mind, topologically massive gravity (TMG) [1] has been widely studied in recent years (see e.g., [2]), which is obtained by adding the gravitational Chern-Simons term to pure Einstein gravity with or without a cosmological constant. For all versions of off-shell N 1⁄4 2 supergravities, the general Killing spinor analysis was given in [14] and all maximally supersymmetric solutions were obtained. The complete field equations of N 1⁄4 ð1; 1Þ GMG were first given in [14] where all maximally supersymmetric solutions were obtained. Linearizing the theory around this vacuum, one finds that, generically, the graviton has two massless modes with η 1⁄4 1 and η 1⁄4 −1 and two massive modes with masses η1 and η2 given by η1η2

Ω η1 þ η2

NULL KILLING VECTOR

TIMELIKE KILLING VECTOR

DISCUSSION