Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

TL;DR

This paper constructs and analyzes classical solutions in Chern-Simons supergravity with superalgebra sl(N|N-1), exploring supersymmetry conditions, explicit solutions, and the existence of smooth supersymmetric conical defects for N≥4.

Contribution

It provides explicit constructions of classical solutions and supersymmetry conditions in Chern-Simons supergravity based on sl(N|N-1), including new solutions and analysis of supersymmetric defects.

Findings

Explicit superalgebra for N=3 constructed.

Killing spinor equations derived and solutions found.

Smooth supersymmetric conical defects exist for N≥4.

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 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\geq 4, the sl(N|N-1) theory admits smooth supersymmetric conical defects.