Abstract
Planar AdS black holes with axionic charge have finite DC conductivity due to momentum relaxation. We obtain a new family of exact asymptotically AdS4 black branes with scalar hair, carrying magnetic and axion charge, and we study the thermodynamics and dynamic stability of these, as well as of a number of previously known electric and dyonic solutions with axion charge and scalar hair. The scalar hair for all solutions satisfy mixed boundary conditions, which lead to modified holographic Ward identities, conserved charges and free energy, relative to those following from the more standard Dirichlet boundary conditions. We show that properly accounting for the scalar boundary conditions leads to well defined first law and other thermodynamic relations. Finally, we compute the holographic quantum effective potential for the dual scalar operator and show that dynamical stability of the hairy black branes is equivalent to positivity of the energy density.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Benincasa, A. Buchel and A.O. Starinets, Sound waves in strongly coupled non-conformal gauge theory plasma, Nucl. Phys. B 733 (2006) 160 [hep-th/0507026] [INSPIRE].
S.I. Finazzo, R. Rougemont, H. Marrochio and J. Noronha, Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography, JHEP 02 (2015) 051 [arXiv:1412.2968] [INSPIRE].
U. Gürsoy, M. Jarvinen and G. Policastro, Late time behavior of non-conformal plasmas, JHEP 01 (2016) 134 [arXiv:1507.08628] [INSPIRE].
M. Attems et al., Thermodynamics, transport and relaxation in non-conformal theories, JHEP 10 (2016) 155 [arXiv:1603.01254] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity, JHEP 01 (2012) 094 [arXiv:1105.1162] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
N. Iizuka, S. Kachru, N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Bianchi Attractors: A Classification of Extremal Black Brane Geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].
Y. Bardoux, M.M. Caldarelli and C. Charmousis, Shaping black holes with free fields, JHEP 05 (2012) 054 [arXiv:1202.4458] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
T. Azeyanagi, W. Li and T. Takayanagi, On String Theory Duals of Lifshitz-like Fixed Points, JHEP 06 (2009) 084 [arXiv:0905.0688] [INSPIRE].
D. Mateos and D. Trancanelli, The anisotropic N = 4 super Yang-Mills plasma and its instabilities, Phys. Rev. Lett. 107 (2011) 101601 [arXiv:1105.3472] [INSPIRE].
S. Jain, N. Kundu, K. Sen, A. Sinha and S.P. Trivedi, A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography, JHEP 01 (2015) 005 [arXiv:1406.4874] [INSPIRE].
A. Donos, J.P. Gauntlett and O. Sosa-Rodriguez, Anisotropic plasmas from axion and dilaton deformations, JHEP 11 (2016) 002 [arXiv:1608.02970] [INSPIRE].
Y. Bardoux, M.M. Caldarelli and C. Charmousis, Conformally coupled scalar black holes admit a flat horizon due to axionic charge, JHEP 09 (2012) 008 [arXiv:1205.4025] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
S.R. Coleman, J. Preskill and F. Wilczek, Quantum hair on black holes, Nucl. Phys. B 378 (1992) 175 [hep-th/9201059] [INSPIRE].
C. Park, On black hole thermodynamics with a momentum relaxation, Class. Quant. Grav. 33 (2016) 245017 [arXiv:1606.07340] [INSPIRE].
I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].
I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP 08 (2005) 004 [hep-th/0505190] [INSPIRE].
T. Hertog and G.T. Horowitz, Designer gravity and field theory effective potentials, Phys. Rev. Lett. 94 (2005) 221301 [hep-th/0412169] [INSPIRE].
V.P. Maslov, Zeroth-Order Phase Transitions, Mat. Zametki 76 (2004) 748.
M. Ibáñez, J. Links, G. Sierra and S.-Y. Zhao, Exactly solvable pairing model for superconductors with a p x + ip y -wave symmetry, Phys. Rev. B 79 (2009) 180501 [arXiv:0810.0340] [INSPIRE].
N. Altamirano, D. Kubiznak and R.B. Mann, Reentrant phase transitions in rotating anti-de Sitter black holes, Phys. Rev. D 88 (2013) 101502 [arXiv:1306.5756] [INSPIRE].
R.M. Wald, General Relativity, The University of Chicago Press (1984).
M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].
S. de Haro, I. Papadimitriou and A.C. Petkou, Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS 4, Phys. Rev. Lett. 98 (2007) 231601 [hep-th/0611315] [INSPIRE].
C. Martinez, R. Troncoso and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70 (2004) 084035 [hep-th/0406111] [INSPIRE].
I. Papadimitriou, Non-Supersymmetric Membrane Flows from Fake Supergravity and Multi-Trace Deformations, JHEP 02 (2007) 008 [hep-th/0606038] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
V. Balasubramanian, P. Kraus and A.E. Lawrence, Bulk versus boundary dynamics in anti-de Sitter space-time, Phys. Rev. D 59 (1999) 046003 [hep-th/9805171] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
I. Papadimitriou, Holographic Renormalization of general dilaton-axion gravity, JHEP 08 (2011) 119 [arXiv:1106.4826] [INSPIRE].
J. Lindgren, I. Papadimitriou, A. Taliotis and J. Vanhoof, Holographic Hall conductivities from dyonic backgrounds, JHEP 07 (2015) 094 [arXiv:1505.04131] [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ’Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
W. Mueck, An improved correspondence formula for AdS/CFT with multitrace operators, Phys. Lett. B 531 (2002) 301 [hep-th/0201100] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
A. Castro, A. Maloney and A. Strominger, Hidden Conformal Symmetry of the Kerr Black Hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [INSPIRE].
S. Bertini, S.L. Cacciatori and D. Klemm, Conformal structure of the Schwarzschild black hole, Phys. Rev. D 85 (2012) 064018 [arXiv:1106.0999] [INSPIRE].
I. Papadimitriou and K. Skenderis, AdS back hole thermodynamics: General boundary conditions for scalars and p-form fields, in preparation.
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
K. Skenderis and P.K. Townsend, Gravitational stability and renormalization group flow, Phys. Lett. B 468 (1999) 46 [hep-th/9909070] [INSPIRE].
D.Z. Freedman, C. Núñez, M. Schnabl and K. Skenderis, Fake supergravity and domain wall stability, Phys. Rev. D 69 (2004) 104027 [hep-th/0312055] [INSPIRE].
I. Papadimitriou and K. Skenderis, Correlation functions in holographic RG flows, JHEP 10 (2004) 075 [hep-th/0407071] [INSPIRE].
D.R. Brill, J. Louko and P. Peldan, Thermodynamics of (3 + 1)-dimensional black holes with toroidal or higher genus horizons, Phys. Rev. D 56 (1997) 3600 [gr-qc/9705012] [INSPIRE].
M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].
L. Vanzo, Black holes with unusual topology, Phys. Rev. D 56 (1997) 6475 [gr-qc/9705004] [INSPIRE].
R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP 06 (1999) 036 [hep-th/9906040] [INSPIRE].
A. Anabalón and D. Astefanesei, On attractor mechanism of AdS 4 black holes, Phys. Lett. B 727 (2013) 568 [arXiv:1309.5863] [INSPIRE].
I. Papadimitriou, Lectures on Holographic Renormalization, Springer Proc. Phys. 176 (2016) 131.
A. Anabalon, D. Astefanesei, D. Choque and C. Martinez, Trace Anomaly and Counterterms in Designer Gravity, JHEP 03 (2016) 117 [arXiv:1511.08759] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1612.07214
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Caldarelli, M.M., Christodoulou, A., Papadimitriou, I. et al. Phases of planar AdS black holes with axionic charge. J. High Energ. Phys. 2017, 1 (2017). https://doi.org/10.1007/JHEP04(2017)001
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2017)001