Supersymmetry of hyperbolic monopoles

Abstract

Abstract:We investigate what supersymmetry says about the geometry of the moduli space of hyperbolic monopoles. We construct a three-dimensional supersymmetric YangMills-Higgs theory on hyperbolic space whose half-BPS configurations coincide with (complexified) hyperbolic monopoles. We then study the action of the preserved supersymmetry on the collective coordinates and show that demanding closure of the supersymmetry algebra constrains the geometry of the moduli space of hyperbolic monopoles, turning it into a so-called pluricomplex manifold, thus recovering a recent result of Bielawski and Schwachhöfer.

Supergravity backgrounds and symmetry superalgebras

“…Structure of these Killing superalgebras in different backgrounds and relations between them give a way to classify these supersymmetric backgrounds. For example, by using the properties of Killing superalgebras, the local homogeneity of a supergravity background that preserves more than half of supersymetries is proved [10,11].…”

“…Moreover, for n = 30 and 31, it is known that there is no supersymmetric supergravity backgrounds [22][23][24][25]. It is also proved that for the cases of ν > 1 2 , those supergravity backgrounds are locally homogeneous [10,11]. For ν = 1, the solutions are called maximally supersymmetric or BPS solutions and examples for this case includes eleven-dimensional flat Minkowski spacetime and Freund-Rubin backgrounds such as AdS 7 × S 4 and AdS 4 × S 7 .…”

“…The classification of all supergravity backgrounds is one of the main goals of the study of supergravity theories. The homogeneity theorem for supergravity backgrounds says that a supergravity background which preserve more then half of the supersymmetries must be homogeneous [10,11]. A homogeneous spacetime can be characterized as a spacetime of which the tangent space at any point is spanned by Killing vectors that are constructed by squaring the Killing spinors of the background.…”

“…To have a well defined Lie superalgebra structure, the Jacobi identities of odd and even parts of the superalgebra must be satisfied. The dimension of the Killing superalgebra is related to the homogeneity structure of the background [10,11]. By constructing the Killing superalgebras of different supergravity backgrounds, one can obtain the geometric and supersymmetric properties of those backgrounds.…”