Abstract
All possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified. Scale invariant geometries where the scalar extremizes its effective potential are distinguished from hyperscaling violating geometries where the scalar runs logarithmically. It is shown that the general critical saddle-point solutions are characterized by three critical exponents (θ, z, ζ). Both exact solutions as well as leading behaviors are exhibited. Using them, neutral or charged geometries realizing both fractionalized or cohesive phases are found. The generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale invariant solutions with a constant scalar.
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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].
A. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565] [INSPIRE].
M. Lassig, Geometry of the renormalization group with an application in two-dimensions, Nucl. Phys. B 334 (1990) 652 [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].
D.T. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].
B. Goutéraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [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].
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].
B.S. Kim, Schródinger Holography with and without Hyperscaling Violation, JHEP 06 (2012) 116 [arXiv:1202.6062] [INSPIRE].
E. Kiritsis, Lorentz violation, Gravity, Dissipation and Holography, JHEP 01 (2013) 030 [arXiv:1207.2325] [INSPIRE].
N. Iizuka, S. Kachru, N. Kundu, P. Narayan, N. Sircar et al., Bianchi Attractors: A Classification of Extremal Black Brane Geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
N. Iizuka, S. Kachru, N. Kundu, P. Narayan, N. Sircar et al., Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes and a Classification for the Homogeneous Case, JHEP 03 (2013) 126 [arXiv:1212.1948] [INSPIRE].
M. Edalati, J.F. Pedraza and W. Tangarife Garcia, Quantum Fluctuations in Holographic Theories with Hyperscaling Violation, Phys. Rev. D 87 (2013) 046001 [arXiv:1210.6993] [INSPIRE].
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, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [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].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008)015 [arXiv:0810.1563] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].
S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A General class of holographic superconductors, JHEP 04 (2010) 092 [arXiv:0906.1214] [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from Superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].
F. Aprile and J.G. Russo, Models of Holographic superconductivity, Phys. Rev. D 81 (2010) 026009 [arXiv:0912.0480] [INSPIRE].
Y. Liu and Y.-W. Sun, Holographic Superconductors from Einstein-Maxwell-Dilaton Gravity, JHEP 07 (2010) 099 [arXiv:1006.2726] [INSPIRE].
A. Salvio, Holographic Superfluids and Superconductors in Dilaton-Gravity, JHEP 09 (2012) 134 [arXiv:1207.3800] [INSPIRE].
U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].
U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].
U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Deconfinement and Gluon Plasma Dynamics in Improved Holographic QCD, Phys. Rev. Lett. 101 (2008) 181601 [arXiv:0804.0899] [INSPIRE].
U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and Thermodynamics of 5D Dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [INSPIRE].
I. Kanitscheider and K. Skenderis, Universal hydrodynamics of non-conformal branes, JHEP 04 (2009) 062 [arXiv:0901.1487] [INSPIRE].
B. Goutéraux, J. Smolic, M. Smolic, K. Skenderis and M. Taylor, Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction, JHEP 01 (2012) 089 [arXiv:1110.2320] [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Semi-local quantum liquids, JHEP 04 (2012) 086 [arXiv:1105.4621] [INSPIRE].
S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].
B.S. Kim, E. Kiritsis and C. Panagopoulos, Holographic quantum criticality and strange metal transport, New J. Phys. 14 (2012) 043045 [arXiv:1012.3464] [INSPIRE].
S.A. Hartnoll and L. Huijse, Fractionalization of holographic Fermi surfaces, Class. Quant. Grav. 29 (2012) 194001 [arXiv:1111.2606] [INSPIRE].
S.A. Hartnoll and R. Pourhasan, Entropy balance in holographic superconductors, JHEP 07 (2012)114 [arXiv:1205.1536] [INSPIRE].
A. Adam, B. Crampton, J. Sonner and B. Withers, Bosonic Fractionalisation Transitions, JHEP 01 (2013) 127 [arXiv:1208.3199] [INSPIRE].
A. Donos and S.A. Hartnoll, Metal-insulator transition in holography, arXiv:1212.2998 [INSPIRE].
T. Faulkner, G.T. Horowitz and M.M. Roberts, New stability results for Einstein scalar gravity, Class. Quant. Grav. 27 (2010) 205007 [arXiv:1006.2387] [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
S.S. Gubser, Curvature singularities: The Good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
K. Goldstein, N. Iizuka, S. Kachru, S. Prakash, S.P. Trivedi and A. Westphal, Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].
E. Perlmutter, Domain Wall Holography for Finite Temperature Scaling Solutions, JHEP 02 (2011)013 [arXiv:1006.2124] [INSPIRE].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].
G.W. Gibbons, K. Hori and P. Yi, String fluid from unstable D-branes, Nucl. Phys. B 596 (2001)136 [hep-th/0009061] [INSPIRE].
C. Charmousis, B. Goutéraux and J. Soda, Einstein-Maxwell-Dilaton theories with a Liouville potential, Phys. Rev. D 80 (2009) 024028 [arXiv:0905.3337] [INSPIRE].
S.A. Hartnoll and E. Shaghoulian, Spectral weight in holographic scaling geometries, JHEP 07 (2012) 078 [arXiv:1203.4236] [INSPIRE].
A. Donos and S.A. Hartnoll, Universal linear in temperature resistivity from black hole superradiance, Phys. Rev. D 86 (2012) 124046 [arXiv:1208.4102] [INSPIRE].
R.J. Anantua, S.A. Hartnoll, V.L. Martin and D.M. Ramirez, The Pauli exclusion principle at strong coupling: Holographic matter and momentum space, JHEP 03 (2013) 104 [arXiv:1210.1590] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Semi-local quantum criticality in string/M-theory, JHEP 03 (2013) 103 [arXiv:1212.1462] [INSPIRE].
S.S. Gubser and F.D. Rocha, The gravity dual to a quantum critical point with spontaneous symmetry breaking, Phys. Rev. Lett. 102 (2009) 061601 [arXiv:0807.1737] [INSPIRE].
S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009)105007 [arXiv:0908.1972] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
D. Cassani and A.F. Faedo, Constructing Lifshitz solutions from AdS, JHEP 05 (2011) 013 [arXiv:1102.5344] [INSPIRE].
W. Chemissany and J. Hartong, From D3-branes to Lifshitz Space-Times, Class. Quant. Grav. 28 (2011) 195011 [arXiv:1105.0612] [INSPIRE].
W. Chemissany, D. Geissbuhler, J. Hartong and B. Rollier, Holographic Renormalization for z=2 Lifshitz Space-Times from AdS, Class. Quant. Grav. 29 (2012) 235017 [arXiv:1205.5777] [INSPIRE].
C. Charmousis, B. Goutéraux and E. Kiritsis, Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography, JHEP 09 (2012) 011 [arXiv:1206.1499] [INSPIRE].
N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi Surfaces and Entanglement Entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].
R. Casero, E. Kiritsis and A. Paredes, Chiral symmetry breaking as open string tachyon condensation, Nucl. Phys. B 787 (2007) 98 [hep-th/0702155] [INSPIRE].
I. Iatrakis, E. Kiritsis and A. Paredes, An AdS/QCD model from Sen’s tachyon action, Phys. Rev. D 81 (2010) 115004 [arXiv:1003.2377] [INSPIRE].
I. Iatrakis, E. Kiritsis and A. Paredes, An AdS/QCD model from tachyon condensation: II, JHEP 11 (2010) 123 [arXiv:1010.1364] [INSPIRE].
M. Jarvinen and E. Kiritsis, Holographic Models for QCD in the Veneziano Limit, JHEP 03 (2012)002 [arXiv:1112.1261] [INSPIRE].
T. Alho, M. Jarvinen, K. Kajantie, E. Kiritsis and K. Tuominen, On finite-temperature holographic QCD in the Veneziano limit, JHEP 01 (2013) 093 [arXiv:1210.4516] [INSPIRE].
D. Arean, I. Iatrakis, M. Jarvinen and E. Kiritsis, V-QCD: Spectra, the dilaton and the S-parameter, Phys. Lett. B 720 (2013) 219 [arXiv:1211.6125] [INSPIRE].
S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz Horizons, arXiv:1202.6635 [INSPIRE].
J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].
N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Entangled Dilaton Dyons, arXiv:1208.2008 [INSPIRE].
A. Adams, A. Maloney, A. Sinha and S.E. Vazquez, 1/N Effects in Non-Relativistic Gauge-Gravity Duality, JHEP 03 (2009) 097 [arXiv:0812.0166] [INSPIRE].
J. Gath, J. Hartong, R. Monteiro and N.A. Obers, Holographic Models for Theories with Hyperscaling Violation, arXiv:1212.3263 [INSPIRE].
G.T. Horowitz and B. Way, Lifshitz Singularities, Phys. Rev. D 85 (2012) 046008 [arXiv:1111.1243] [INSPIRE].
E. Shaghoulian, Holographic Entanglement Entropy and Fermi Surfaces, JHEP 05 (2012) 065 [arXiv:1112.2702] [INSPIRE].
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Goutéraux, B., Kiritsis, E. Quantum critical lines in holographic phases with (un)broken symmetry. J. High Energ. Phys. 2013, 53 (2013). https://doi.org/10.1007/JHEP04(2013)053
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DOI: https://doi.org/10.1007/JHEP04(2013)053