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

TL;DR

This paper investigates conditions for partial supersymmetry breaking in ${ m extbf{N}=2}$ supergravity with one hypermultiplet, showing the uniqueness of Minkowski solutions and exploring more general AdS cases.

Contribution

It proves the uniqueness of Minkowski partial breaking solutions in this setting and constructs new AdS solutions, extending previous models.

Findings

No other Minkowski partial breaking solutions exist beyond known examples.

Partial-breaking vacua in AdS are more generic and less constrained.

Constructed explicit solutions on specific quaternion-Kähler manifolds.

Abstract

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 $SO(4,1)/SO(4)$. We demonstrate that no other example of partial breaking of ${\cal N}=2$ supergravity in Minkowski spacetime exists. We also examine partial-breaking vacua in anti-de Sitter spacetime that are much less constrained and exist generically even for electric gaugings. On $SO(4,1)/SO(4)$, we construct the partially-broken solution and its global limit which is the Antoniadis-Partouche-Taylor model.