6D attractors and black hole microstates

Abstract

We find a family of AdS 2 ×M 4 supersymmetric solutions of the six-dimensional F(4) gauged supergravity coupled to one vector multiplet that arises as a low energy description of massive type IIA supergravity on (warped) AdS 6 × S 4 . M 4 is either a Kähler-Einstein manifold or a product of two Riemann surfaces with a constant curvature metric. These solutions correspond to the near-horizon region of a family of static magnetically charged black holes. In the case where M 4 is a product of Riemann surfaces, we successfully compare their entropy to a microscopic counting based on the recently computed topologically twisted index of the five-dimensional N = 1 USp(2N ) theory with N f fundamental flavors and an antisymmetric matter field. Furthermore, our results suggest that the near-horizon regions exhibit an attractor mechanism for the scalars in the matter coupled F(4) gauged supergravity, and we give a proposal for it.Recently there has been some progress in understanding the microscopic origin of the Bekenstein-Hawking entropy of supersymmetric asymptotically anti-de Sitter (AdS) black holes. In particular, the microscopic entropy of certain four-dimensional static, dyonic, BPS black holes [1][2][3][4][5], which can be embedded in AdS 4 × S 7 , has been reproduced by a field theory calculation based on the topologically twisted index [6] of the dual ABJM theory in the large N limit [7-9]. These black holes have an AdS 2 × Σ g near-horizon geometry, where Σ g is a Riemann surface of genus g. The topologically twisted index is the partition function of the dual field theory on Σ g × S 1 , partially topologically A-twisted along Σ g . Specifically, the index Z(p I , ∆ I ) is a function of a set of magnetic charges p I and complexified chemical potentials ∆ I for the global symmetries of the theory. The statistical entropy S BH of the black holes with purely magnetic charges is then obtained by evaluating Z(p I , ∆ I ) at its critical point∆ I :

Gluing gravitational blocks for AdS black holes

“…We consider here black holes in the AdS 6 × w S 4 background of massive type IIA supergravity [47]. For KN-AdS 6 [44], mAdS 6 [46,75] and possible rotating generalizations with near horizon AdS 2 × w M 4 , where the manifold M 4 is either S 4 or toric Kähler, we should use 16…”

“…We now show that we can reproduce the above entropy functional by gluing six-dimensional gravitational blocks. Unfortunately, there are no regular black hole solutions with manifolds M 4 of positive curvature [46], as one can see by extremizing (6.12). Nevertheless, it makes sense to consider all kind of horizons because we want to reproduce the functional form of I smAdS 6 (p I , ∆ I ), independently of whether it has acceptable critical points or not.…”

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

“…Indeed, comparing to (3.8) we find precise agreement. As discussed around (1.2)-(1.4), to account for the entropy of 11 Approaching the origin from above, ω → i0 + , the dominant saddle is instead the flat connection A . The final answer is the same and the limit is well defined.…”

“…This was first achieved for five-dimensional black holes in asymptotically flat spacetime in the seminal work [1]. For black holes in asymptotically locally AdS spacetimes this has only been recently achieved, starting with certain magnetic black holes in 4d in [2], extended in various ways in [3][4][5][6][7], for magnetic black holes in 6d in [8][9][10][11][12][13], and for spinning black holes in 5d in [14][15][16][17][18][19]. These calculations rely on holography, exploiting the properties of the asymptotic SCFT dual and the powerful supersymmetric localization techniques developed in the past decade.…”

Exact results for 5d SCFTs of long quiver type

“…These theories have been studied extensively e.g. in [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. However, many more 5d gauge theories are believed to have strongly-coupled UV fixed points, and indeed many more theories can be engineered in Type IIB string theory using 5-brane webs [3][4][5], 5-brane webs with 7-branes [29] and further generalizations [30][31][32][33].…”