Holographic studies of Einsteinian cubic gravity
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Springer
Received: February Revised: March Accepted: March Published: March
14, 19, 21, 26,
2018 2018 2018 2018
Holographic studies of Einsteinian cubic gravity
a
Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium b Instituto de F´ısica Te´ orica UAM/CSIC, C/ Nicol´ as Cabrera, 13-15, C.U. Cantoblanco, 28049 Madrid, Spain c Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
E-mail: [email protected], [email protected], [email protected] Abstract: Einsteinian cubic gravity provides a holographic toy model of a nonsupersymmetric CFT in three dimensions, analogous to the one defined by Quasi-topological gravity in four. The theory admits explicit non-hairy AdS4 black holes and allows for numerous exact calculations, fully nonperturbative in the new coupling. We identify several entries of the AdS/CFT dictionary for this theory, and study its thermodynamic phase space, finding interesting new phenomena. We also analyze the dependence of R´enyi entropies for disk regions on universal quantities characterizing the CFT. In addition, we show that η/s is given by a non-analytic function of the ECG coupling, and that the existence of positive-energy black holes strictly forbids violations of the KSS bound. Along the way, we introduce a new method for evaluating Euclidean on-shell actions for general higherorder gravities possessing second-order linearized equations on AdS(d+1) . Our generalized action involves the very same Gibbons-Hawking boundary term and counterterms valid for Einstein gravity, which now appear weighted by the universal charge a∗ controlling the entanglement entropy across a spherical region in the CFT dual to the corresponding higher-order theory. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Black Holes in String Theory ArXiv ePrint: 1802.00018
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)150
JHEP03(2018)150
Pablo Bueno,a Pablo A. Canob,c and Alejandro Ruip´ erezb
Contents 1 Introduction 1.1 Summary of results
1 2
2 Einsteinian cubic gravity 2.1 AdS4 vacua and linearized spectrum
4 5 7 8 9 10
4 Generalized action for higher-order gravities 4.1 a∗ and generalized action 4.2 Generalized action for Quasi-topological gravity 4.3 Generalized action for Einsteinian cubic gravity
12 15 16 17
5 Stress tensor two-point function charge CT
17
6 Thermodynamics 6.1 Entropy, energy and free energy 6.2 Thermal entropy charge CS 6.3 Toroidal boundary: black brane vs AdS4 soliton 6.4 Spherical boundary: Hawking-Page transitions
21 21 23 24 25
7 R´ enyi entropy 7.1 Holographic R´enyi entropy 7.2 Scaling dimension of twist operators 7.3 Stress tensor three-point function charge t4
29 29 34 35
8 Holographic hydrodynamics
36
9 Final comments 9.1 Generalized action, a∗ and holographic complexity?
41 42
A hT T T i parameters from hq A.1 Gauss-Bonnet in arbitrary dimensions A.2 Quasi-topological gravity
43 43 44
B Generalized action for Gauss-Bonnet gravi
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