Bogomol'nyi Bounds and Killing Spinors in d=3 Supergravity

TL;DR

This paper explores how Bogomol'nyi bounds and equations in 3D supergravity relate to underlying N=2 supersymmetry, enabling the construction of Killing spinors in asymptotically conical spacetimes and linking topological bounds to supercovariantly constant spinors.

Contribution

It demonstrates that a first order gravitational equation derived from local supersymmetry can bypass previous no-go results for Killing spinors in certain spacetimes.

Findings

Existence of supercovariantly constant spinors when topological bounds are saturated.

A first order gravitational equation consistent with Einstein equations can be derived from supersymmetry.

Evasion of no-go scenarios for Killing spinors in asymptotically conical spacetimes.

Abstract

We discuss the connection between the construction of Bogomol'nyi bounds and equations in three dimensional gravitational theories and the existence of an underlying $N=2$ local supersymmetric structure. We show that, appart from matter self duality equations, a first order equation for the gravitational field (whose consistency condition gives the Einstein equation) can be written as a consequence of the local supersymmetry. Its solvability makes possible the evasion of the no-go scenario for the construction of Killing spinors in asymptotically conical spacetimes. In particular we show that the existence of non-trivial supercovariantly constant spinors is guaranteed whenever field configurations saturate the topological bound.