Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

Abstract

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N|N − 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal ${{\mathcal{W}}_3}$ superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N − 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N ≥ 4, the sl(N|N − 1) theory admits smooth supersymmetric conical defects.