Abstract
We consider partial supersymmetry breaking in mathcal{N}=2 supergravity coupled to a single vector and a single hypermultiplet. This breaking pattern is in principle possible if the quaternion-Kähler 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 mathcal{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.
Highlights
Which the SU(2)R symmetry is violated by electric and magnetic Fayet-Iliopoulos (FI) terms inducing a nonlinear deformation of the second supersymmetry variation of one gaugino, defining it as the goldstino
We consider partial supersymmetry breaking in N = 2 supergravity coupled to a single vector and a single hypermultiplet
We perform a general analysis of the N = 2 partial breaking in supergravity theories containing a single hypermultiplet with two commuting isometries, gauged by the graviphoton and an additional vector multiplet
Summary
An electric gauging of two translation isometries of the hypermultiplet manifold SO(4, 1)/SO(4) ∼ Sp(2, 2)/SU(2) × SU(2) in this non-prepotential frame leads to a two-coupling theory with zero potential and N = 0 for generic values of the couplings, N = 1 when a linear relation is verified by the couplings, and N = 2 for zero couplings. With the graviphoton and the gauge field of a vector multiplet (nV = 1), we can gauge two commuting isometries, as required if partial supersymmetry breaking is envisaged [13] This implies that two commuting isometries should exist and this defines a class of scalar manifolds for a single hypermultiplet for which explicit metrics are available. We find useful to express the scalar potential (2.37) in terms of the anti-selfdual covariant derivatives ka−uv defined in appendix A:
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