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Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity. (English) Zbl 1390.83155

Summary: We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Hořava gravity with Lifshitz exponent \(z=1\) . As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the holographic dictionary should be modified to deal with the multiple horizons and differing propagation speeds of bulk excitations in Hořava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Hořava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.

MSC:

83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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[1] Maldacena, JM, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113, (1999) · Zbl 0969.81047 · doi:10.1023/A:1026654312961
[2] Policastro, G.; Son, DT; Starinets, AO, From AdS/CFT correspondence to hydrodynamics, JHEP, 09, 043, (2002) · doi:10.1088/1126-6708/2002/09/043
[3] G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. 2. Sound waves, JHEP12 (2002) 054 [hep-th/0210220] [INSPIRE].
[4] Bhattacharyya, S.; Hubeny, VE; Minwalla, S.; Rangamani, M., Nonlinear fluid dynamics from gravity, JHEP, 02, 045, (2008) · doi:10.1088/1126-6708/2008/02/045
[5] Grozdanov, S.; Kaplis, N.; Starinets, AO, From strong to weak coupling in holographic models of thermalization, JHEP, 07, 151, (2016) · Zbl 1390.83113 · doi:10.1007/JHEP07(2016)151
[6] Policastro, G.; Son, DT; Starinets, AO, the shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett., 87, 081601, (2001) · doi:10.1103/PhysRevLett.87.081601
[7] Kovtun, P.; Son, DT; Starinets, AO, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett., 94, 111601, (2005) · doi:10.1103/PhysRevLett.94.111601
[8] Buchel, A.; Liu, JT; Starinets, AO, coupling constant dependence of the shear viscosity in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys., B 707, 56, (2005) · Zbl 1160.81463 · doi:10.1016/j.nuclphysb.2004.11.055
[9] Buchel, A., Resolving disagreement for η/s in a CFT plasma at finite coupling, Nucl. Phys., B 803, 166, (2008) · Zbl 1190.81115 · doi:10.1016/j.nuclphysb.2008.05.024
[10] Myers, RC; Paulos, MF; Sinha, A., Quantum corrections to η/s, Phys. Rev., D 79, 041901, (2009)
[11] Kovtun, PK; Starinets, AO, Quasinormal modes and holography, Phys. Rev., D 72, 086009, (2005)
[12] Benincasa, P.; Buchel, A., transport properties of N = 4 supersymmetric Yang-Mills theory at finite coupling, JHEP, 01, 103, (2006) · doi:10.1088/1126-6708/2006/01/103
[13] Baier, R.; Romatschke, P.; Son, DT; Starinets, AO; Stephanov, MA, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP, 04, 100, (2008) · Zbl 1246.81352 · doi:10.1088/1126-6708/2008/04/100
[14] Buchel, A., Shear viscosity of boost invariant plasma at finite coupling, Nucl. Phys., B 802, 281, (2008) · Zbl 1190.82042 · doi:10.1016/j.nuclphysb.2008.03.009
[15] Buchel, A.; Paulos, M., Relaxation time of a CFT plasma at finite coupling, Nucl. Phys., B 805, 59, (2008) · Zbl 1190.76173 · doi:10.1016/j.nuclphysb.2008.07.002
[16] Buchel, A.; Paulos, M., Second order hydrodynamics of a CFT plasma from boost invariant expansion, Nucl. Phys., B 810, 40, (2009) · Zbl 1192.81296 · doi:10.1016/j.nuclphysb.2008.10.012
[17] Saremi, O.; Sohrabi, KA, Causal three-point functions and nonlinear second-order hydrodynamic coefficients in AdS/CFT, JHEP, 11, 147, (2011) · Zbl 1306.81169 · doi:10.1007/JHEP11(2011)147
[18] Grozdanov, S.; Starinets, AO, On the universal identity in second order hydrodynamics, JHEP, 03, 007, (2015) · Zbl 1317.83068 · doi:10.1007/JHEP03(2015)007
[19] Grozdanov, S.; Kaplis, N., Constructing higher-order hydrodynamics: the third order, Phys. Rev., D 93, 066012, (2016)
[20] Kolekar, KS; Mukherjee, D.; Narayan, K., Hyperscaling violation and the shear diffusion constant, Phys. Lett., B 760, 86, (2016) · Zbl 1398.83095 · doi:10.1016/j.physletb.2016.06.046
[21] J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE]. · Zbl 1325.81004
[22] Hartnoll, SA; Kovtun, PK; Muller, M.; Sachdev, S., Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev., B 76, 144502, (2007) · doi:10.1103/PhysRevB.76.144502
[23] Taylor, M., Lifshitz holography, Class. Quant. Grav., 33, 033001, (2016) · Zbl 1332.83004 · doi:10.1088/0264-9381/33/3/033001
[24] Son, DT, Toward an AdS/cold atoms correspondence: A geometric realization of the Schrödinger symmetry, Phys. Rev., D 78, 046003, (2008)
[25] Balasubramanian, K.; McGreevy, J., Gravity duals for non-relativistic cfts, Phys. Rev. Lett., 101, 061601, (2008) · Zbl 1228.81247 · doi:10.1103/PhysRevLett.101.061601
[26] Balasubramanian, K.; Narayan, K., Lifshitz spacetimes from AdS null and cosmological solutions, JHEP, 08, 014, (2010) · Zbl 1291.83195 · doi:10.1007/JHEP08(2010)014
[27] Janiszewski, S.; Karch, A., String theory embeddings of nonrelativistic field theories and their holographic Hořava gravity duals, Phys. Rev. Lett., 110, 081601, (2013) · doi:10.1103/PhysRevLett.110.081601
[28] Janiszewski, S.; Karch, A., Non-relativistic holography from Hořava gravity, JHEP, 02, 123, (2013) · doi:10.1007/JHEP02(2013)123
[29] Hořava, P., Quantum gravity at a Lifshitz point, Phys. Rev., D 79, 084008, (2009)
[30] Hartong, J.; Obers, NA, Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry, JHEP, 07, 155, (2015) · Zbl 1388.83586 · doi:10.1007/JHEP07(2015)155
[31] D.T. Son, Newton-Cartan Geometry and the Quantum Hall Effect, arXiv:1306.0638 [INSPIRE].
[32] K. Jensen, On the coupling of Galilean-invariant field theories to curved spacetime, arXiv:1408.6855 [INSPIRE].
[33] Hartong, J.; Kiritsis, E.; Obers, NA, Schrödinger invariance from Lifshitz isometries in holography and field theory, Phys. Rev., D 92, 066003, (2015)
[34] Fuini, JF; Karch, A.; Uhlemann, CF, Spinor fields in general Newton-Cartan backgrounds, Phys. Rev., D 92, 125036, (2015)
[35] Janiszewski, S., Asymptotically hyperbolic black holes in Hořava gravity, JHEP, 01, 018, (2015) · Zbl 1388.83469 · doi:10.1007/JHEP01(2015)018
[36] Blas, D.; Sibiryakov, S., Hořava gravity versus thermodynamics: the black hole case, Phys. Rev., D 84, 124043, (2011)
[37] Barausse, E.; Jacobson, T.; Sotiriou, TP, Black holes in Einstein-aether and Hořava-Lifshitz gravity, Phys. Rev., D 83, 124043, (2011)
[38] Berglund, P.; Bhattacharyya, J.; Mattingly, D., Mechanics of universal horizons, Phys. Rev., D 85, 124019, (2012)
[39] Berglund, P.; Bhattacharyya, J.; Mattingly, D., Towards thermodynamics of universal horizons in Einstein-æther theory, Phys. Rev. Lett., 110, 071301, (2013) · doi:10.1103/PhysRevLett.110.071301
[40] Bhattacharyya, J.; Mattingly, D., Universal horizons in maximally symmetric spaces, Int. J. Mod. Phys., D 23, 1443005, (2014) · Zbl 1314.83038 · doi:10.1142/S0218271814430056
[41] Jensen, K.; Karch, A., Revisiting non-relativistic limits, JHEP, 04, 155, (2015) · Zbl 1388.83355 · doi:10.1007/JHEP04(2015)155
[42] Eling, C.; Oz, Y., Hořava-Lifshitz black hole hydrodynamics, JHEP, 11, 067, (2014) · Zbl 1333.83073 · doi:10.1007/JHEP11(2014)067
[43] Son, DT; Starinets, AO, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP, 09, 042, (2002) · doi:10.1088/1126-6708/2002/09/042
[44] Herzog, CP; Son, DT, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP, 03, 046, (2003) · doi:10.1088/1126-6708/2003/03/046
[45] Skenderis, K.; Rees, BC, Real-time gauge/gravity duality, Phys. Rev. Lett., 101, 081601, (2008) · Zbl 1228.81244 · doi:10.1103/PhysRevLett.101.081601
[46] Skenderis, K.; Rees, BC, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP, 05, 085, (2009) · doi:10.1088/1126-6708/2009/05/085
[47] L P. Kadanoff and P.C. Martin, Hydrodynamic equations and correlation functions, Annals Phys.24 (1963) 419.
[48] Kovtun, P., Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys., A 45, 473001, (2012) · Zbl 1348.83039
[49] Jensen, K.; Kaminski, M.; Kovtun, P.; Meyer, R.; Ritz, A.; Yarom, A., Parity-violating hydrodynamics in 2+1 dimensions, JHEP, 05, 102, (2012) · doi:10.1007/JHEP05(2012)102
[50] Kaminski, M.; Moroz, S., Nonrelativistic parity-violating hydrodynamics in two spatial dimensions, Phys. Rev., B 89, 115418, (2014) · doi:10.1103/PhysRevB.89.115418
[51] Jensen, K., Aspects of hot Galilean field theory, JHEP, 04, 123, (2015) · Zbl 1388.83354 · doi:10.1007/JHEP04(2015)123
[52] Hoyos, C.; Kim, BS; Oz, Y., Lifshitz hydrodynamics, JHEP, 11, 145, (2013) · doi:10.1007/JHEP11(2013)145
[53] Hoyos, C.; Kim, BS; Oz, Y., Lifshitz field theories at non-zero temperature, hydrodynamics and gravity, JHEP, 03, 029, (2014) · doi:10.1007/JHEP03(2014)029
[54] Hoyos, C.; Kim, BS; Oz, Y., Ward identities for transport in 2+1 dimensions, JHEP, 03, 164, (2015) · Zbl 1388.83016 · doi:10.1007/JHEP03(2015)164
[55] Hoyos, C.; Meyer, A.; Oz, Y., Parity breaking transport in Lifshitz hydrodynamics, JHEP, 09, 031, (2015) · Zbl 1388.83353 · doi:10.1007/JHEP09(2015)031
[56] Kiritsis, E.; Matsuo, Y., Charge-hyperscaling violating Lifshitz hydrodynamics from black-holes, JHEP, 12, 076, (2015) · Zbl 1388.81388 · doi:10.1007/JHEP12(2015)076
[57] J. Zaanen, Y. Liu, Y.-W. Sun, and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, Cambridge, U.K. (2015). · doi:10.1017/CBO9781139942492
[58] Griffin, T.; Hořava, P.; Melby-Thompson, CM, Lifshitz gravity for Lifshitz holography, Phys. Rev. Lett., 110, 081602, (2013) · Zbl 1348.83074 · doi:10.1103/PhysRevLett.110.081602
[59] D.T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas, Annals Phys.321 (2006) 197 [cond-mat/0509786] [INSPIRE]. · Zbl 1107.82419
[60] Herzog, CP, The hydrodynamics of M-theory, JHEP, 12, 026, (2002) · doi:10.1088/1126-6708/2002/12/026
[61] T. Jacobson and D. Mattingly, Gravity with a dynamical preferred frame, Phys. Rev.D 64 (2001) 024028 [gr-qc/0007031] [INSPIRE]. · Zbl 1104.83307
[62] Blas, D.; Pujolàs, O.; Sibiryakov, S., Models of non-relativistic quantum gravity: the good, the bad and the healthy, JHEP, 04, 018, (2011) · Zbl 1250.83031 · doi:10.1007/JHEP04(2011)018
[63] Germani, C.; Kehagias, A.; Sfetsos, K., Relativistic quantum gravity at a Lifshitz point, JHEP, 09, 060, (2009) · doi:10.1088/1126-6708/2009/09/060
[64] B.Z. Foster, Metric redefinitions in Einstein-Aether theory, Phys. Rev.D 72 (2005) 044017 [gr-qc/0502066] [INSPIRE].
[65] Haro, S.; Solodukhin, SN; Skenderis, K., Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys., 217, 595, (2001) · Zbl 0984.83043 · doi:10.1007/s002200100381
[66] Balakin, AB; Lemos, JPS, Einstein-aether theory with a Maxwell field: general formalism, Annals Phys., 350, 454, (2014) · Zbl 1344.83037 · doi:10.1016/j.aop.2014.07.024
[67] Herzog, CP, The sound of M-theory, Phys. Rev., D 68, 024013, (2003)
[68] Davison, RA; Goutéraux, B.; Hartnoll, SA, Incoherent transport in Clean quantum critical metals, JHEP, 10, 112, (2015) · Zbl 1388.81933 · doi:10.1007/JHEP10(2015)112
[69] Iqbal, N.; Liu, H., Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev., D 79, 025023, (2009)
[70] Gürsoy, U.; Tarrio, J., Horizon universality and anomalous conductivities, JHEP, 10, 058, (2015) · Zbl 1388.81935 · doi:10.1007/JHEP10(2015)058
[71] Grozdanov, S.; Poovuttikul, N., Universality of anomalous conductivities in theories with higher-derivative holographic duals, JHEP, 09, 046, (2016) · Zbl 1390.83112 · doi:10.1007/JHEP09(2016)046
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