Abstract
We consider asymptotically AdS black brane solutions that are dual to CFTs with periodic dependence on the spatial directions, arising from either a spontaneous or an explicit breaking of translational symmetry. We derive a simple expression for the variation of the free-energy with respect to changing the periods. This explains some observations, based on numerics, that have arisen in the explicit construction of thermodynamically preferred black holes in the case that the spatial directions are infinite in extent and the symmetry is spontaneously broken. It also leads to Smarr-type relations involving the boundary stress tensor.
Similar content being viewed by others
References
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D 86 (2012) 064010 [arXiv:1204.1734] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic helical superconductors, JHEP 12 (2011) 091 [arXiv:1109.3866] [INSPIRE].
A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett. 108 (2012) 211601 [arXiv:1203.0533] [INSPIRE].
S.K. Domokos and J.A. Harvey, Baryon number-induced Chern-Simons couplings of vector and axial-vector mesons in holographic QCD, Phys. Rev. Lett. 99 (2007) 141602 [arXiv:0704.1604] [INSPIRE].
N. Iizuka et al., Bianchi attractors: a classification of extremal black brane geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
M. Rozali, D. Smyth, E. Sorkin and J.B. Stang, Holographic stripes, Phys. Rev. Lett. 110 (2013) 201603 [arXiv:1211.5600] [INSPIRE].
A. Donos, Striped phases from holography, JHEP 05 (2013) 059 [arXiv:1303.7211] [INSPIRE].
B. Withers, Black branes dual to striped phases, arXiv:1304.0129 [INSPIRE].
B. Withers, The moduli space of striped black branes, arXiv:1304.2011 [INSPIRE].
M. Rozali, D. Smyth, E. Sorkin and J.B. Stang, Striped order in AdS/CFT, Phys. Rev. D 87 (2013) 126007 [arXiv:1304.3130] [INSPIRE].
O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Striped instability of a holographic Fermi-like liquid, JHEP 10 (2011) 034 [arXiv:1106.3883] [INSPIRE].
A. Aperis et al., Holographic charge density waves, Phys. Lett. B 702 (2011) 181 [arXiv:1009.6179] [INSPIRE].
R. Flauger, E. Pajer and S. Papanikolaou, A Striped Holographic Superconductor, Phys. Rev. D 83 (2011) 064009 [arXiv:1010.1775] [INSPIRE].
K. Maeda, T. Okamura and J.-i. Koga, Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime, Phys. Rev. D 85 (2012) 066003 [arXiv:1107.3677] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Further evidence for lattice-induced scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].
A. Donos and S.A. Hartnoll, Metal-insulator transition in holography, arXiv:1212.2998 [INSPIRE].
G.T. Horowitz and J.E. Santos, General relativity and the cuprates, arXiv:1302.6586 [INSPIRE].
B. Mahmoud El-Menoufi, B. Ett, D. Kastor and J. Traschen, Gravitational Tension and Thermodynamics of Planar AdS Spacetimes, Class. Quant. Grav. 30 (2013) 155003 [arXiv:1302.6980] [INSPIRE].
B. Mahmoud El-Menoufi, B. Ett, D. Kastor and J. Traschen, Sum Rule for the ADM Mass and Tensions in Planar AdS Spacetimes, arXiv:1305.1913 [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP 08 (2005) 004 [hep-th/0505190] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, The thermodynamics of Kaluza-Klein black hole/bubble chains, Class. Quant. Grav. 25 (2008) 125004 [arXiv:0803.2019] [INSPIRE].
E. D’Hoker and P. Kraus, Charged magnetic brane solutions in AdS 5 and the fate of the third law of thermodynamics, JHEP 03 (2010) 095 [arXiv:0911.4518] [INSPIRE].
J.H. Traschen and D. Fox, Tension perturbations of black brane space-times, Class. Quant. Grav. 21 (2004) 289 [gr-qc/0103106] [INSPIRE].
P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Hard-gapped Holographic Superconductors, Phys. Lett. B 689 (2010) 45 [arXiv:0911.4999] [INSPIRE].
M. Ammon, J. Erdmenger, V. Grass, P. Kerner and A. O’Bannon, On Holographic p-wave Superfluids with Back-reaction, Phys. Lett. B 686 (2010) 192 [arXiv:0912.3515] [INSPIRE].
S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].
J. Erdmenger, A.-K. Straub and H. Zeller, private communication.
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].
M. Ammon, J. Erdmenger, P. Kerner and M. Strydom, Black hole instability induced by a magnetic field, Phys. Lett. B 706 (2011) 94 [arXiv:1106.4551] [INSPIRE].
A. Almuhairi and J. Polchinski, Magnetic AdS × R 2 : supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and Electric AdS Solutions in String- and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].
A. Donos, J.P. Gauntlett, J. Sonner and B. Withers, Competing orders in M-theory: superfluids, stripes and metamagnetism, JHEP 03 (2013) 108 [arXiv:1212.0871] [INSPIRE].
A. Almheiri, Magnetic AdS 2 × R 2 at Weak and Strong Coupling, arXiv:1112.4820 [INSPIRE].
Y.-Y. Bu, J. Erdmenger, J.P. Shock and M. Strydom, Magnetic field induced lattice ground states from holography, JHEP 03 (2013) 165 [arXiv:1210.6669] [INSPIRE].
N. Bao, S. Harrison, S. Kachru and S. Sachdev, Vortex lattices and crystalline geometries, Phys. Rev. D 88 (2013) 026002 [arXiv:1303.4390] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
C. Charmousis, B. Gouteraux, B. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [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].
S. Cremonini and A. Sinkovics, Spatially modulated instabilities of geometries with hyperscaling violation, arXiv:1212.4172 [INSPIRE].
N. Iizuka and K. Maeda, Stripe instabilities of geometries with hyperscaling violation, Phys. Rev. D 87 (2013) 126006 [arXiv:1301.5677] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic charge density waves, Phys. Rev. D 87 (2013) 126008 [arXiv:1303.4398] [INSPIRE].
N. Bao and S. Harrison, Crystalline scaling geometries from vortex lattices, Phys. Rev. D 88 (2013) 046009 [arXiv:1306.1532] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Donos, A., Gauntlett, J.P. On the thermodynamics of periodic AdS black branes. J. High Energ. Phys. 2013, 38 (2013). https://doi.org/10.1007/JHEP10(2013)038
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2013)038