Supergravity and a Bogomolʹnyi bound in three dimensions Original Research Article

We discuss the (2 + 1)-dimensional Abelian Higgs model coupled to N = 2 supergravity. The model provides an example on how unbroken supercharges can be defined, circumventing the problem of finding supercovariantly constant Killing spinors in 2+1 dimensions. We show that this is due to the existence of gravitating vortices saturating a Bogomolʹnyi bound. The corresponding self-duality equations imply, through an integrability condition, the Einstein equation.