Squashing the boundary of supersymmetric AdS5 black holes

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 AdS 5 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 S 5 and should thus be dual to N = 4 super Yang-Mills on a rotating, squashed Einstein universe. arXiv:1809.02149v3 [hep-th] 17 Dec 2018 1 See also [24] for a non-supersymmetric study.

The BPS limit of rotating AdS black hole thermodynamics

“…In five dimensions, there are also recently found black holes that are just asymptotically locally AdS 5 , since the S 3 spatial part of the conformal boundary is squashed [56][57][58]. It has been shown in [57] that the expression of the Bekenstein-Hawking entropy of these black holes in terms of the charges is the same as in the round S 3 case, provided one uses the Page electric charges of the solution. Hence the entropy function should also be the same, provided the electric potentials ϕ I are those conjugate to the Page charges.…”

“…whereQ IJ is the kinetic matrix evaluated on the supersymmetric AdS 5 vacuum, and ϕ I (0) is the coefficient of the O(r −2 ) term in the expansion of the scalar fields X I . We refer to [57] for details on the derivation of these quantities in general asymptotically locally AdS 5 solutions to Fayet-Iliopoulos gauged supergravity.…”

“…Since the limit is smooth, these BPS chemical potentials still satisfy the constraint 57) and the on-shell action of the BPS solution reads…”

“…In this appendix, we evaluate the holographic charges and the on-shell action of the AdS 5 black holes studied in Section 2. In order to remove the divergences due to the infinite spacetime volume we adopt holographic renormalization and use the counterterms for Fayet-Iliopoulos gauged supergravity given in [57].…”

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes

“…These multi-charge solutions feature running scalar fields, and it will be interesting to investigate whether the extremization of the on-shell action is related to a five-dimensional attractor mechanism for the scalars as suggested in [23]. It will also be worth considering the recently constructed asymptotically locally AdS 5 black holes with a squashed boundary [80,81]. The squashing deformations studied in these papers should not affect the SCFT partition function, so one could expect the story to work similarly to the case with no squashing; however the subtleties related to the non-trivial gauge field at the boundary noted in [81] deserve a careful study.…”