Abstract
We construct a family of holographic duals to anisotropic states in a strongly coupled gauge theory. On the field theory side the anisotropy is generated by giving a vacuum expectation value to a dimension three operator. We obtain our gravity duals by considering the geometry corresponding to the intersection of D3- and D5- branes along 2+1 dimensions. Our backgrounds are supersymmetric and solve the fully backreacted equations of motion of ten-dimensional supergravity with smeared D5-brane sources. In all cases the geometry flows to AdS5× 𝕊5 in the UV, signaling an isotropic UV fixed point of the dual field theory. In the IR, depending on the parameters of the solution, we find two possible behaviors: an isotropic fixed point or a geometry with anisotropic Lifshitz-like scaling symmetry. We study several properties of the solutions, including the entanglement entropy of strips. We show that any natural extension of existing c-functions will display non-monotonic behavior, conforming with the presence of new degrees of freedom only at intermediate regions between the boundary and the origin of the holographic dual.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.A. Janik and P. Witaszczyk, Towards the description of anisotropic plasma at strong coupling, JHEP09 (2008) 026 [arXiv:0806.2141] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett.102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].
K. Yagi and N. Yunes, Relating follicly-challenged compact stars to bald black holes: a link between two no-hair properties, Phys. Rev.D 91 (2015) 103003 [arXiv:1502.04131] [INSPIRE].
K. Yagi and N. Yunes, I-love-Q relations: from compact stars to black holes, Class. Quant. Grav.33 (2016) 095005 [arXiv:1601.02171] [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].
D. Mateos and D. Trancanelli, Thermodynamics and instabilities of a strongly coupled anisotropic plasma, JHEP07 (2011) 054 [arXiv:1106.1637] [INSPIRE].
J.-i. Koga, K. Maeda and K. Tomoda, Holographic superconductor model in a spatially anisotropic background, Phys. Rev.D 89 (2014) 104024 [arXiv:1401.6501] [INSPIRE].
S. Jain, N. Kundu, K. Sen, A. Sinha and S.P. Trivedi, A strongly coupled anisotropic fluid from dilaton driven holography, JHEP01 (2015) 005 [arXiv:1406.4874] [INSPIRE].
E. Banks and J.P. Gauntlett, A new phase for the anisotropic N = 4 super Yang-Mills plasma, JHEP09 (2015) 126 [arXiv:1506.07176] [INSPIRE].
D. Roychowdhury, On anisotropic black branes with Lifshitz scaling, Phys. Lett.B 759 (2016) 410 [arXiv:1509.05229] [INSPIRE].
D. Roychowdhury, Holography for anisotropic branes with hyperscaling violation, JHEP01 (2016) 105 [arXiv:1511.06842] [INSPIRE].
V. Jahnke and A.S. Misobuchi, Probing strongly coupled anisotropic plasmas from higher curvature gravity, Eur. Phys. J.C 76 (2016) 309 [arXiv:1510.03774] [INSPIRE].
E. Banks, Phase transitions of an anisotropic N = 4 super Yang-Mills plasma via holography, JHEP07 (2016) 085 [arXiv:1604.03552] [INSPIRE].
D. Ávila, D. Fernández, L. Patiño and D. Trancanelli, Thermodynamics of anisotropic branes, JHEP11 (2016) 132 [arXiv:1609.02167] [INSPIRE].
A. Donos, J.P. Gauntlett and O. Sosa-Rodriguez, Anisotropic plasmas from axion and dilaton deformations, JHEP11 (2016) 002 [arXiv:1608.02970] [INSPIRE].
D. Giataganas, U. Gürsoy and J.F. Pedraza, Strongly-coupled anisotropic gauge theories and holography, Phys. Rev. Lett.121 (2018) 121601 [arXiv:1708.05691] [INSPIRE].
G. Itsios, N. Jokela, J. Järvelä and A.V. Ramallo, Low-energy modes in anisotropic holographic fluids, Nucl. Phys.B 940 (2019) 264 [arXiv:1808.07035] [INSPIRE].
I. Aref’eva and K. Rannu, Holographic anisotropic background with confinement-deconfinement phase transition, JHEP05 (2018) 206 [arXiv:1802.05652] [INSPIRE].
P. Liu, C. Niu and J.-P. Wu, The effect of anisotropy on holographic entanglement entropy and mutual information, Phys. Lett.B 796 (2019) 155 [arXiv:1905.06808] [INSPIRE].
G.A. Inkof et al., Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points, arXiv:1907.05744 [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Finite temperature large N gauge theory with quarks in an external magnetic field, JHEP07 (2008) 080 [arXiv:0709.1547] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Quarks in an external electric field in finite temperature large N gauge theory, JHEP08 (2008) 092 [arXiv:0709.1554] [INSPIRE].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP12 (2007) 091 [arXiv:0709.1551] [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic brane solutions in AdS, JHEP10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
E. D’Hoker and P. Kraus, Charged magnetic brane solutions in AdS5and the fate of the third law of thermodynamics, JHEP03 (2010) 095 [arXiv:0911.4518] [INSPIRE].
K. Jensen, A. Karch and E.G. Thompson, A holographic quantum critical point at finite magnetic field and finite density, JHEP05 (2010) 015 [arXiv:1002.2447] [INSPIRE].
N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Phase diagram of the D3/D5 system in a magnetic field and a BKT transition, Phys. Lett.B 698 (2011) 91 [arXiv:1003.2694] [INSPIRE].
E. D’Hoker and P. Kraus, Holographic metamagnetism, quantum criticality and crossover behavior, JHEP05 (2010) 083 [arXiv:1003.1302] [INSPIRE].
K.-Y. Kim, B. Sahoo and H.-U. Yee, Holographic chiral magnetic spiral, JHEP10 (2010) 005 [arXiv:1007.1985] [INSPIRE].
C. Hoyos, T. Nishioka and A. O’Bannon, A chiral magnetic effect from AdS/CFT with flavor, JHEP10 (2011) 084 [arXiv:1106.4030] [INSPIRE].
M. Ammon, V.G. Filev, J. Tarrio and D. Zoakos, D3/D7 quark-gluon plasma with magnetically induced anisotropy, JHEP09 (2012) 039 [arXiv:1207.1047] [INSPIRE].
U. Gürsoy, M. Järvinen, G. Nijs and J.F. Pedraza, Inverse anisotropic catalysis in holographic QCD, JHEP04 (2019) 071 [arXiv:1811.11724] [INSPIRE].
N. Evans, K.-Y. Kim, J.P. Shock and J.P. Shock, Chiral phase transitions and quantum critical points of the D3/D7(D5) system with mutually perpendicular E and B fields at finite temperature and density, JHEP09 (2011) 021 [arXiv:1107.5053] [INSPIRE].
D.E. Kharzeev and H.-U. Yee, Chiral helix in AdS/CFT with flavor, Phys. Rev.D 84 (2011) 125011 [arXiv:1109.0533] [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].
N. Jokela and A.V. Ramallo, Universal properties of cold holographic matter, Phys. Rev.D 92 (2015) 026004 [arXiv:1503.04327] [INSPIRE].
G. Itsios, N. Jokela and A.V. Ramallo, Collective excitations of massive flavor branes, Nucl. Phys.B 909 (2016) 677 [arXiv:1602.06106] [INSPIRE].
S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP11 (2008) 033 [arXiv:0805.2960] [INSPIRE].
M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Superconductivity from gauge/gravity duality with flavor, Phys. Lett.B 680 (2009) 516 [arXiv:0810.2316] [INSPIRE].
P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Superconductivity from D3/D7: holographic pion superfluid, JHEP11 (2009) 070 [arXiv:0810.3970] [INSPIRE].
N. Iizuka et al., Bianchi attractors: a classification of extremal black brane geometries, JHEP07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett.108 (2012) 211601 [arXiv:1203.0533] [INSPIRE].
N. Iizuka and K. Maeda, Study of Anisotropic Black Branes in Asymptotically anti-de Sitter, JHEP07 (2012) 129 [arXiv:1204.3008] [INSPIRE].
C. Hoyos, D. Rodríguez Fernández, N. Jokela and A. Vuorinen, Holographic quark matter and neutron stars, Phys. Rev. Lett.117 (2016) 032501 [arXiv:1603.02943] [INSPIRE].
E. Annala et al., Holographic compact stars meet gravitational wave constraints, JHEP12 (2018) 078 [arXiv:1711.06244] [INSPIRE].
N. Jokela, M. Järvinen and J. Remes, Holographic QCD in the Veneziano limit and neutron stars, JHEP03 (2019) 041 [arXiv:1809.07770] [INSPIRE].
T. Ishii, M. Järvinen and G. Nijs, Cool baryon and quark matter in holographic QCD, JHEP07 (2019) 003 [arXiv:1903.06169] [INSPIRE].
P.M. Chesler, N. Jokela, A. Loeb and A. Vuorinen, Finite-temperature equations of state for neutron star mergers, Phys. Rev.D 100 (2019) 066027 [arXiv:1906.08440] [INSPIRE].
K. Zhang, T. Hirayama, L.-W. Luo and F.-L. Lin, Compact star of holographic nuclear matter and GW170817, Phys. Lett.B 801 (2020) 135176 [arXiv:1902.08477] [INSPIRE].
C. Ecker, M. Järvinen, G. Nijs and W. van der Schee, Gravitational waves from holographic neutron star mergers, arXiv:1908.03213 [INSPIRE].
K. Bitaghsir Fadafan, J. Cruz Rojas and N. Evans, Deconfined, massive quark phase at high density and compact stars, arXiv:1911.12705 [INSPIRE].
E. Fradkin et al., Nematic Fermi fluids in condensed matter physics, Annu. Rev. Cond. Matt. Phys.1 (2010) 153 [arXiv:0910.4166].
J.M. Penin, A.V. Ramallo and D. Zoakos, Anisotropic D3-D5 black holes with unquenched flavors, JHEP02 (2018) 139 [arXiv:1710.00548] [INSPIRE].
N. Jokela, J.M. Penín, A.V. Ramallo and D. Zoakos, Gravity dual of a multilayer system, JHEP03 (2019) 064 [arXiv:1901.02020] [INSPIRE].
U. Gran, N. Jokela, D. Musso, A.V. Ramallo and M. Tornsö, Holographic fundamental matter in multilayered media, JHEP12 (2019) 038 [arXiv:1909.01864] [INSPIRE].
A. Donos, J.P. Gauntlett, C. Rosen and O. Sosa-Rodriguez, Boomerang RG flows in M-theory with intermediate scaling, JHEP07 (2017) 128 [arXiv:1705.03000] [INSPIRE].
A. Donos, J.P. Gauntlett, C. Rosen and O. Sosa-Rodriguez, Boomerang RG flows with intermediate conformal invariance, JHEP04 (2018) 017 [arXiv:1712.08017] [INSPIRE].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys.3 (1999) 363 [hep-th/9904017] [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett.43 (1986) 730 [INSPIRE].
H. Casini and M. Huerta, A finite entanglement entropy and the c-theorem, Phys. Lett.B 600 (2004) 142 [hep-th/0405111] [INSPIRE].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev.D 82 (2010) 046006 [arXiv:1006.1263] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev.D 85 (2012) 125016 [arXiv:1202.5650] [INSPIRE].
E. Conde, J. Gaillard, C. Núñez, M. Piai and A.V. Ramallo, Towards the string dual of tumbling and cascading gauge theories, Phys. Lett.B 709 (2012) 385 [arXiv:1112.3346] [INSPIRE].
E. Conde et al., A tale of two cascades: Higgsing and Seiberg-duality cascades from type IIB string theory, JHEP02 (2012) 145 [arXiv:1112.3350] [INSPIRE].
A. Donos and J.P. Gauntlett, Flowing from AdS5to AdS3with T1,1 , JHEP08 (2014) 006 [arXiv:1404.7133] [INSPIRE].
J.P. Gauntlett and C. Rosen, Susy Q and spatially modulated deformations of ABJM theory, JHEP10 (2018) 066 [arXiv:1808.02488] [INSPIRE].
I. Arav, J.P. Gauntlett, M. Roberts and C. Rosen, Spatially modulated and supersymmetric deformations of ABJM theory, JHEP04 (2019) 099 [arXiv:1812.11159] [INSPIRE].
C. Núñez, A. Paredes and A.V. Ramallo, Unquenched flavor in the gauge/gravity correspondence, Adv. High Energy Phys.2010 (2010) 196714 [arXiv:1002.1088] [INSPIRE].
E. Conde et al., D3-D5 theories with unquenched flavors, Nucl. Phys.B 914 (2017) 599 [arXiv:1607.04998] [INSPIRE].
O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev.D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].
S.S. Gubser, S.S. Pufu and F.D. Rocha, Quantum critical superconductors in string theory and M-theory, Phys. Lett.B 683 (2010) 201 [arXiv:0908.0011] [INSPIRE].
J.T. Liu and Z. Zhao, Holographic Lifshitz flows and the null energy condition, arXiv:1206.1047 [INSPIRE].
S. Cremonini and X. Dong, Constraints on renormalization group flows from holographic entanglement entropy, Phys. Rev.D 89 (2014) 065041 [arXiv:1311.3307] [INSPIRE].
Y. Bea et al., Compactifications of the Klebanov-Witten CFT and new AdS3backgrounds, JHEP05 (2015) 062 [arXiv:1503.07527] [INSPIRE].
C.-S. Chu and D. Giataganas, c-theorem for anisotropic RG flows from holographic entanglement entropy, Phys. Rev.D 101 (2020) 046007 [arXiv:1906.09620] [INSPIRE].
M. Ghasemi and S. Parvizi, Constraints on anisotropic RG flows from holographic entanglement entropy, arXiv:1907.01546 [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP08 (2006) 045 [hep-th/0605073] [INSPIRE].
P.A.R. Jones and M. Taylor, Entanglement entropy in top-down models, JHEP08 (2016) 158 [arXiv:1602.04825] [INSPIRE].
V. Sahakian, Holography, a covariant c function and the geometry of the renormalization group, Phys. Rev.D 62 (2000) 126011 [hep-th/9910099] [INSPIRE].
R. Bousso, A Covariant entropy conjecture, JHEP07 (1999) 004 [hep-th/9905177] [INSPIRE].
E. Alvarez and C. Gomez, Geometric holography, the renormalization group and the c theorem, Nucl. Phys.B 541 (1999) 441 [hep-th/9807226] [INSPIRE].
Y. Bea, E. Conde, N. Jokela and A.V. Ramallo, Unquenched massive flavors and flows in Chern-Simons matter theories, JHEP12 (2013) 033 [arXiv:1309.4453] [INSPIRE].
V. Balasubramanian, N. Jokela, A. Pönni and A.V. Ramallo, Information flows in strongly coupled ABJM theory, JHEP01 (2019) 232 [arXiv:1811.09500] [INSPIRE].
N. Jokela and A. Pönni, Notes on entanglement wedge cross sections, JHEP07 (2019) 087 [arXiv:1904.09582] [INSPIRE].
A.G. Grushin, Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals, Phys. Rev.D 86 (2012) 045001 [arXiv:1205.3722] [INSPIRE].
F. Benini et al., Unquenched flavors in the Klebanov-Witten model, JHEP02 (2007) 090 [hep-th/0612118] [INSPIRE].
F. Benini et al., Backreacting flavors in the Klebanov-Strassler background, JHEP09 (2007) 109 [arXiv:0706.1238] [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: 2001.08218
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Hoyos, C., Jokela, N., Penín, J.M. et al. Holographic spontaneous anisotropy. J. High Energ. Phys. 2020, 62 (2020). https://doi.org/10.1007/JHEP04(2020)062
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2020)062