All partial breakings in ${\cal N}=2$ supergravity with a single hypermultiplet

Understand

We consider partial supersymmetry breaking in ${\cal N}=2$ supergravity coupled to a single vector and a single hypermultiplet.

• This breaking pattern is in principle possible if the quaternion-K\"ahler space of the hypermultiplet admits (at least) one pair of commuting isometries.
• For this class of manifolds, explicit metrics exist and we analyse a generic electro-magnetic (dyonic) gauging of the isometries.
• An example of partial breaking in Minkowski spacetime has been found long ago by Ferrara, Girardello and Porrati, using the gauging of two translation isometries on $SO(4,1)/SO(4)$.