Abstract
Abstract We establish a relation between the structure governing four- and five- dimensional black holes and multicenter solutions on the one hand and Calabi-Yau flux compactifications of M-theory and type IIB string theory on the other hand, for both supersymmetric and non-supersymmetric solutions. We find that the known BPS and almost-BPS multicenter black hole solutions can be interpreted as GKP compactifications with (2,1) and (0,3) imaginary self-dual flux. We also show that the most general GKP compactification leads to new classes of BPS and non-BPS multicenter solutions. We explore how these solutions fit into N = 2 truncations, and elucidate how supersymmetry becomes camouflaged. As a necessary tool in our exploration we show how the fields in the largest N = 2 truncation fit inside the six-torus compactification of eleven-dimensional supergravity.
Highlights
A first step towards relating these two research currents has been taken in [19], where we found that certain supersymmetric flux backgrounds of the type [20] whose “internal” manifold contains a hyper-Kahler factor are related to non-rotating solutions in the classification of [4,5,6]
The first purpose of this paper is to deepen the relation between supersymmetric flux compactifications and multicenter solutions found in [19], and to show that this relation extends to non-supersymmetric solutions: some of the non-supersymmetric IIB and Mtheory flux compactifications of [1, 2, 21] can be reinterpreted as almost-BPS multicenter solutions [7, 22,23,24], while some others give new solutions that lie outside of the almost-BPS class and in general have more dipole charges
We give an overview of the relation of BPS and almost-BPS solutions in the STU model to flux compactifications in figure 1
Summary
In this paper we mainly consider M-theory compactified on a six-dimensional torus T 6. This leads to a five-dimensional “maximal” supergravity, (with 32 supercharges), which we will denote by N = 8 supergravity. The purpose of this section is to discuss the “largest” truncation of this five-dimensional N = 8 supergravity to N = 2 supergravity (with 8 supercharges), in terms of the eleven-dimensional fields and the geometry of the internal space.
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