On the on-shell: the action of AdS 4 black holes
- PDF / 407,878 Bytes
- 18 Pages / 595.276 x 841.89 pts (A4) Page_size
- 100 Downloads / 152 Views
Springer
Received: December 7, 2017 Accepted: March 10, 2018 Published: March 26, 2018
Nick Halmagyib,a and Shailesh Lala a
Sorbonne Universit´es, UPMC Paris 06, UMR 7589, LPTHE, 75005, Paris, France b CNRS, UMR 7589, LPTHE, 75005, Paris, France
E-mail: [email protected], [email protected] Abstract: We compute the on-shell action of static, BPS black holes in AdS4 from N = 2 gauged supergravity coupled to vector multiplets and show that for a certain class it is equal to minus the entropy of the black hole. Holographic renormalization is used to demonstrate that with Neumann boundary conditions on the scalar fields, the divergent and finite contributions from the asymptotic boundary vanish. The entropy arises from the extrinsic curvature on Σg × S 1 evaluated at the horizon, where Σg may have any genus g ≥ 0. This provides a clarification of the equivalence between the partition function of the twisted ABJM theory on Σg × S 1 and the entropy of the dual black hole solutions. It also demonstrates that the complete entropy resides on the AdS2 × Σg horizon geometry, implying the absence of hair for these gravity solutions. Keywords: AdS-CFT Correspondence, Black Holes, Black Holes in String Theory ArXiv ePrint: 1710.09580
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)146
JHEP03(2018)146
On the on-shell: the action of AdS4 black holes
Contents 1
2 Supersymmetric black holes in AdS4 2.1 N = 2 FI-gauged supergravity 2.2 The black hole ansatz 2.3 BPS solutions 2.4 AdS4 boundary conditions 2.5 STU model 2.6 Universal black hole
2 2 3 4 5 5 6
3 Holographic free energy 3.1 On-shell action, a first look 3.2 BPS form of the action 3.3 Cancellation of divergences 3.4 Finite action from the boundary 3.5 The complete on shell action
7 7 8 9 10 12
4 Conclusions
13
A Special geometry background
13
1
Introduction
Holography has provided a robust framework for explaining the Bekenstein-Hawking entropy of a black hole from microscopic considerations. For black holes in asymptotically flat space-times, the essential breakthrough was [1] but the subsequent development of AdS/CFT [2] has lead to a far deeper understanding of this line of research. The starting point of such work is typically supersymmetric black holes and in AdS 4 , static-BPS black holes with spherical horizon were only found somewhat recently [3]. In [4, 5] the entropy of these black holes1 has been reproduced from the holographically dual field theory using fundamentally different methods than those employed in [1]; namely by localization and without recourse to the Cardy formula of a two-dimensional CFT. The purpose of the current work is to further clarify the relationship between the macroscopic computations of the entropy and the microscopic calculations of [4, 5]. The holographic dictionary relates the boundary partition function to the on-shell action of the gravitational theory, not the entropy. In this work we consider supersymmetric (and extremal) dyonically charged black holes
Data Loading...
