Exploring Three-dimensional Higher-Spin Supergravity based on sl(N |N - 1) Chern-Simons theories

Abstract

We investigate various aspects of higher-spin anti-de Sitter supergravity in three dimensions as described by Chern-Simons theory based on the finite-dimensional superalgebra sl(N |N - 1), with the particular case of N = 3 as our prime example. This class of theories serves as a natural supersymmetrization of the higher-spin gravity theory based on sl(N) Chern-Simons theories. We demonstrate explicitly that the asymptotic symmetry algebra contains the N = 2 superconformal algebra in each sector. The appropriate Killing spinor equations are derived and used to classify existing and new classical solutions. We also discuss holonomy conditions, higher-spin black holes and conical defect spacetimes in this class of theories.