The BPS limit of rotating AdS black hole thermodynamics

124

We provide a unifying entropy functional and an extremization principle for black holes and black strings in AdS 4 × S 7 and AdS 5 × S 5 with arbitrary rotation and generic electric and magnetic charges. This is done by gluing gravitational blocks, basic building blocks that are directly inspired by the holomorphic blocks appearing in the factorization of supersymmetric partition functions in three and four dimensions. We also provide an explicit realization of the attractor mechanism by identifying the values of the scalar fields at the horizon with the critical points of the entropy functional. We give examples based on dyonic rotating black holes with a twist in AdS 4 × S 7 , rotating black strings in AdS 5 × S 5 , dyonic Kerr-Newman black holes in AdS 4 × S 7 and Kerr-Newman black holes in AdS 5 × S 5 . In particular, our entropy functional extends existing results by adding rotation to the twisted black holes in AdS 4 and by adding flavor magnetic charges for the Kerr-Newman black holes in AdS 4 . We also discuss generalizations to higher-dimensional black objects. arXiv:1909.10550v1 [hep-th] 23 Sep 20191 The BPS conditions impose a linear constraint on the magnetic charges and some non-linear con-5 This has been checked at large N in full generality for static mAdS 4 black holes [1,41], rotating black strings in AdS 5 [19], KN-AdS 5 black holes with equal angular momenta [4] and at large N but in the Cardy limit for general purely electric KN-AdS 4 and KN-AdS 5 [3,42]. It is still not known if the large N limit of the superconformal index of N = 4 SYM reproduces the entropy functional, and therefore the entropy, in the case of KN-AdS 5 black holes with unequal angular momenta.6 See also [43] for a different approach.10 In particular, in the regime considered in (4.15) the minus sign in the chemical potential is equivalent to a complex conjugate. This might explain the complex conjugate we detect in gravity, see (4.9). 11 We correct a misprint in the formula for the entropy in [21]. Note also that we have redefined the angular momentum as J there = − 1 2 J here (see footnote 21).An important symmetry of the equations of motion of supergravity is the electromagnetic duality. As the name suggests, the n V + 1 electric and magnetic gauge field strengths F Λ and G Λ (Λ = 0, . . . , n V ) can be transformed among each other under the symplectic group Sp(2(n V + 1), Z), resulting in a rotation of the electromagnetic charges,

Section: Discussion and Outlookmentioning

confidence: 90%

mentioning

confidence: 99%

Gluing gravitational blocks for AdS black holes

Hosseini

Hristov

Zaffaroni

2019

124

“…The thermodynamics of this black hole was discussed in some detail in [41] and more recently in [42][43][44]. One can define chemical potentials for the angular momentum and the gauge field, which are given by…”

Section: )mentioning

confidence: 99%

“…Note that since in Euclidean signature a is taken to purely imaginary, this requires a complex δ. One can show that supersymmetry implies a constraint among the chemical potentials Ω, Φ [44]:…”

Section: Supersymmetry and Extremalitymentioning

confidence: 99%

See 1 more Smart Citation

Universal spinning black holes and theories of class $$ \mathcal{R} $$

Bobev

Crichigno

2019

We study a supersymmetric, rotating, electrically charged black hole in AdS 4 which is a solution of four-dimensional minimal gauged supergravity. Using holography we show that the free energy on S 3 and the superconformal index of the dual three-dimensional N = 2 SCFT, in the planar limit, are related in a simple universal way. This result applies to large classes of SCFTs constructed from branes in string and M-theory which we discuss in some detail. For theories of class R, which arise from N M5-branes wrapped on hyperbolic three-manifolds, we show that the superconformal index agrees with the black hole entropy in the large N limit. arXiv:1909.05873v2 [hep-th]

AdS7 black-hole entropy and 5D $$ \mathcal{N} $$ = 2 Yang-Mills

Kántor

Papageorgakis

Richmond

2020

We generalise the work of 1810.11442 for the case of AdS 7 /CFT 6 . Starting from the 2equivalent charge, 3-equivalent rotation non-extremal black-hole solution in 7D gauged supergravity, we consider the supersymmetric and then the extremal limit and evaluate the associated thermodynamic quantities. Away from extremality, the black-hole solution becomes complex. The entropy is then given by the Legendre transform of the on-shell action with respect to two complex chemical potentials subject to a constraint. At the conformal boundary we derive the dual background and evaluate the corresponding partition function for the A N −1 6D (2,0) theory at large N in a Cardy-like limit. This is carried out via a 5D N = 2 super Yang-Mills calculation on S 5 . The gravitational on-shell action is found to be exactly reproduced by the boundary partition function at large N. We argue that this agreement puts strong constraints on the form of possible higher-derivative corrections to the 5D gauge theory that is used in the S 5 evaluation.