Rotating attractors and BPS black holes in AdS4

We discuss the Cardy limit of 3d supersymmetric partition functions which allow the factorization into the hemisphere indices: the generalized superconformal index, the refined topologically twisted index and the squashed sphere partition function. In the Cardy limit, the hemisphere index can be evaluated by the saddle point approximation where there exists a dominant saddle point contribution, which we call the Cardy block. The Cardy block turns out to be a simple but powerful object as it is a building block of other partition functions in the Cardy limit. The factorization to the Cardy block allows us to find universal relations among the partition functions, which we formulate as index theorems. Furthermore, if we consider a holographic 3d SCFT and its large N limit, those partition functions relate to various entropic quantities of the dual gravity theory in AdS 4 . As a result, our result provides the microscopic derivation of the universal relations among those entropic quantities of the gravity theory. We also discuss explicit examples, which confirm our general index theorems.

Section: The Refined Topologically Twisted Indexmentioning

confidence: 72%

Section: The Refined Topologically Twisted Indexmentioning

confidence: 99%

Universal 3d Cardy block and black hole entropy

Choi

Hwang

2020

“…There have been many studies regarding rotating magnetically charged black holes that are the natural candidates for the refined topologically twisted index. In particular, there is one recent publication that discusses these issues in detail and contains a comprehensive list of references [64]. A common theme, since the very beginning of the explorations of rotating magnetically charged black holes, is that within the confines of the universal sector described by the action in equation (4.12) spherically symmetric black holes do not exist [59].…”

Section: Rotating Magnetically Charged Ads 4 Black Holesmentioning

confidence: 99%

Rotating black hole entropy from M5-branes

Benini

Gang

Zayas

2020

We compute the superconformal index of 3d N = 2 superconformal theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence we use perturbative invariants of SL(N, C) Chern-Simons theory to determine the superconformal index in the large N limit, including logarithmic in N corrections. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS 4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We also propose a 3d-3d formulation for the refined topologically twisted index and provide strong evidence in support of its vanishing which agrees with the fact that the expected dual rotating magnetically charged black hole does not exist, thus providing an interesting link between gravity and a tantalizing mathematical result. 3d T N [M 3 ] theoryWe start with the definition and basic properties of the 3d T N [M 3 ] theory appearing on the LHS of the 3d-3d relation (2.1). We define T N [M 3 ] := the 3d N = 2 superconformal field theory obtained from a twisted compactification of the 6d A N −1 (2,0) theory on M 3 , M 3 = a closed hyperbolic 3-manifold = H 3 /Γ .(2.2)

“…We conclude with discussion and outlook in section 7. Appendix A contains some technical aspects of the relevant N = 2 gauged supergravity and the black hole solutions of [17,21]. Appendix B contains an example of our techniques applied to asymptotically flat black holes in four dimensions.…”

Section: Figure 1 Gluing Gravitational Blocksmentioning

confidence: 99%

“…In order to give a unifying picture it is convenient to use a four-dimensional point of view. All the above mentioned black objects can be dimensionally reduced to give four-dimensional rotating black hole solutions of an N = 2 gauged supergravity coupled to vector multiplets that can be studied using the methods in [17,21]. The relevant gauged supergravity arises as a consistent truncation of type IIB or M-theory and it is completely specified by a prepotential F(X Λ ) and a set of gauging, or Fayet-Iliopoulos parameters, {g Λ , g Λ }.…”

mentioning

confidence: 99%

Gluing gravitational blocks for AdS black holes

Hosseini

Hristov

Zaffaroni

2019

Self Cite

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,