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arXiv · 1006.0239

All the timelike supersymmetric solutions of all ungauged d=4 supergravities

P. Meessen·T. Ortin·S. Vaula
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Abstract

We determine the form of all timelike supersymmetric solutions of all N greater or equal than 2, d=4 ungauged supergravities, for N less or equal than 4 coupled to vector supermultiplets, using the $Usp(n+1,n+1)-symmetric formulation of Andrianopoli, D'Auria and Ferrara and the spinor-bilinears method, while preserving the global symmetries of the theories all the way. As previously conjectured in the literature, the supersymmetric solutions are always associated to a truncation to an N=2 theory that may include hypermultiplets, although fields which are eliminated in the truncations can have non-trivial values, as is required by the preservation of the global symmetry of the theories. The solutions are determined by a number of independent functions, harmonic in transverse space, which is twice the number of vector fields of the theory (n+1). The transverse space is flat if an only if the would-be hyperscalars of the associated N=2 truncation are trivial.

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P. Meessen, T. Ortin, S. Vaula. 2010-06-01. All the timelike supersymmetric solutions of all ungauged d=4 supergravities. https://doi.org/10.1007/jhep11(2010)072

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