Abstract
We construct new supersymmetric black holes in five-dimensional supergravity with an arbitrary number of vector multiplets and Fayet-Iliopoulos gauging. These are asymptotically locally AdS5 and the conformal boundary comprises a squashed three-sphere with SU(2) × U(1) symmetry. The solution depends on two parameters, of which one determines the angular momentum and the Page electric charges, while the other controls the squashing at the boundary. The latter is arbitrary, however in the flow towards the horizon it is attracted to a value that only depends on the other parameter of the solution. The entropy is reproduced by a simple formula involving the angular momentum and the Page charges, rather than the holographic charges. Choosing the appropriate five-dimensional framework, the solution can be uplifted to type IIB supergravity on S5 and should thus be dual to mathcal{N} = 4 super Yang-Mills on a rotating, squashed Einstein universe.
Highlights
Been extended to further examples of AdS4 black holes in M-theory and massive type IIA string theory e.g. in [4,5,6,7,8,9], while subleading corrections in the large N expansion have been investigated for example in [10]
Very recently an interesting observation has been made [17], that the entropy of the known supersymmetric AdS5 black holes is reproduced by extremizing a quantity which appears to be closely related to the supersymmetric Casimir energy of four-dimensional superconformal field theories (SCFT’s) on S1 × S3 [18,19,20]
We find that of the two parameters, one controls the event horizon geometry as well as the angular momentum and the Page electric charges of the solution, while the other is responsible for the squashing at the boundary and does not affect the horizon
Summary
We provide a brief summary and proceed to partially solve such conditions after imposing a simplifying ansatz In this way we will be left with just two ODE’s, generalizing the single ODE obtained in [11] for the minimal gauged supergravity theory. We have expressed XI , f and U I in terms of a and HI We use these findings to manipulate eq (2.24) containing w and the Maxwell equation (2.26), following a strategy used in section 4 of [11] in the context of minimal gauged supergravity. We conclude that our equations (2.43), (2.47) provide a direct generalization of the minimal supersymmetry equation of [11] to the case with an arbitrary number of vector multiplets, where both the gauge and the scalar fields are running
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