Abstract
We use gauge-gravity duality to study the transport properties of a finite density of charge carriers in a strongly-coupled theory with non-relativistic symmetry. The field theory is \( \mathcal{N} = 4 \) supersymmetric SU(N c ) Yang-Mills theory in the limit of large N c and with large ’t Hooft coupling, deformed by an irrelevant operator, coupled to a number N f of massive \( \mathcal{N}{ = 4} \) supersymmetric hypermultiplets in the fundamental representation of the gauge group, i.e. flavor fields. The irrelevant deformation breaks the relativistic conformal group down to the Schrödinger group, which has non-relativistic scale invariance with dynamical exponent z = 2. Introducing a finite baryon number density of the flavor fields provides us with charge carriers. We compute the associated DC and AC conductivities using the dual gravitational description of probe D7-branes in an asymptotically Schrödinger spacetime. We generically find that in the infrared the conductivity exhibits scaling with temperature or frequency that is relativistic, while in the ultraviolet the scalings appear to be non-relativistic with dynamical exponent z = 2, as expected in the presence of the irrelevant deformation.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
T. Mehen, I.W. Stewart and M.B. Wise, Conformal invariance for non-relativistic field theory, Phys. Lett. B 474 (2000) 145 [hep-th/9910025] [SPIRES].
Y. Nishida and D.T. Son, Nonrelativistic conformal field theories, Phys. Rev. D 76 (2007) 086004 [arXiv:0706.3746] [SPIRES].
D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [SPIRES].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].
C. Duval, G.W. Gibbons and P. Horvathy, Celestial Mechanics, Conformal Structures and Gravitational Waves, Phys. Rev. D 43 (1991) 3907 [hep-th/0512188] [SPIRES].
C. Duval, M. Hassaine and P.A. Horvathy, The geometry of Schródinger symmetry in gravity background/non-relativistic CFT, Annals Phys. 324 (2009) 1158 [arXiv:0809.3128] [SPIRES].
C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [SPIRES].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non- relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [SPIRES].
A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [SPIRES].
A. Adams, C.M. Brown, O. DeWolfe and C. Rosen, Charged Schrödinger Black Holes, Phys. Rev. D 80 (2009) 125018 [arXiv:0907.1920] [SPIRES].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [SPIRES].
A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys. Rev. D 76 (2007) 086007 [arXiv:0708.1994] [SPIRES].
M. Ammon, T.H. Ngo and A. O’Bannon, Holographic Flavor Transport in Arbitrary Constant Background Fields, JHEP 10 (2009) 027 [arXiv:0908.2625] [SPIRES].
R.C. Myers, A.O. Starinets and R.M. Thomson, Holographic spectral functions and diffusion constants for fundamental matter, JHEP 11 (2007) 091 [arXiv:0706.0162] [SPIRES].
D. Mateos and L. Patino, Bright branes for strongly coupled plasmas, JHEP 11 (2007) 025 [arXiv:0709.2168] [SPIRES].
J. Mas, J.P. Shock, J. Tarrio and D. Zoakos, Holographic Spectral Functions at Finite Baryon Density, JHEP 09 (2008) 009 [arXiv:0805.2601] [SPIRES].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [SPIRES].
S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].
M.C.N. Cheng, S.A. Hartnoll and C.A. Keeler, Deformations of Lifshitz holography, JHEP 03 (2010) 062 [arXiv:0912.2784] [SPIRES].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [SPIRES].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavour, JHEP 07 (2003) 049 [hep-th/0304032] [SPIRES].
J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in non-supersymmetric gauge / gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [SPIRES].
I. Kirsch, Generalizations of the AdS/CFT correspondence, Fortsch. Phys. 52 (2004) 727 [hep-th/0406274] [SPIRES].
S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [SPIRES].
N. Bobev, A. Kundu and K. Pilch, Supersymmetric IIB Solutions with Schródinger Symmetry, JHEP 07 (2009) 107 [arXiv:0905.0673] [SPIRES].
A. Donos and J.P. Gauntlett, Solutions of type IIB and D = 11 supergravity with Schrödinger(z) symmetry, JHEP 07 (2009) 042 [arXiv:0905.1098] [SPIRES].
E.G. Gimon, A. Hashimoto, V.E. Hubeny, O. Lunin and M. Rangamani, Black strings in asymptotically plane wave geometries, JHEP 08 (2003) 035 [hep-th/0306131] [SPIRES].
J.L.F. Barbon and C.A. Fuertes, Ideal gas matching for thermal Galilean holography, Phys. Rev. D 80 (2009) 026006 [arXiv:0903.4452] [SPIRES].
C.A. Fuertes and S. Moroz, Correlation functions in the non-relativistic AdS/CFT correspondence, Phys. Rev. D 79 (2009) 106004 [arXiv:0903.1844] [SPIRES].
A. Volovich and C. Wen, Correlation Functions in Non-Relativistic Holography, JHEP 05 (2009) 087 [arXiv:0903.2455] [SPIRES].
R.C. Myers, Dielectric-branes, JHEP 12 (1999) 022 [hep-th/9910053] [SPIRES].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [SPIRES].
S.S. Pal, Null Melvin Twist to Sakai-Sugimoto model, arXiv:0808.3042 [SPIRES].
A. Karch and A. O’Bannon, Holographic Thermodynamics at Finite Baryon Density: Some Exact Results, JHEP 11 (2007) 074 [arXiv:0709.0570] [SPIRES].
A. Karch, A. O’Bannon and K. Skenderis, Holographic renormalization of probe D-branes in AdS/CFT, JHEP 04 (2006) 015 [hep-th/0512125] [SPIRES].
I. Kirsch, Spectroscopy of fermionic operators in AdS/CFT, JHEP 09 (2006) 052 [hep-th/0607205] [SPIRES].
R.G. Leigh and N.N. Hoang, Fermions and the Sch/nrCFT Correspondence, JHEP 03 (2010) 027 [arXiv:0909.1883] [SPIRES].
D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [SPIRES].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Quarks in an External Electric Field in Finite Temperature Large-N Gauge Theory, JHEP 08 (2008) 092 [arXiv:0709.1554] [SPIRES].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [SPIRES].
J. Erdmenger, M. Kaminski and F. Rust, Holographic vector mesons from spectral functions at finite baryon or isospin density, Phys. Rev. D 77 (2008) 046005 [arXiv:0710.0334] [SPIRES].
J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals - A Review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [SPIRES].
J. Erdmenger, M. Kaminski, P. Kerner and F. Rust, Finite baryon and isospin chemical potential in AdS/CFT with flavor, JHEP 11 (2008) 031 [arXiv:0807.2663] [SPIRES].
C.P. Burgess, Open string instability in background electric fields, Nucl. Phys. B 294 (1987) 427 [SPIRES].
C. Bachas and M. Porrati, Pair creation of open strings in an electric field, Phys. Lett. B 296 (1992) 77 [hep-th/9209032] [SPIRES].
N. Seiberg, A note on background independence in noncommutative gauge theories, matrix model and tachyon condensation, JHEP 09 (2000) 003 [hep-th/0008013] [SPIRES].
J. Mas, J.P. Shock and J. Tarrio, On the Einstein Relation in holographic systems at finite baryon density, Nucl. Phys. Proc. Suppl. 192-193 (2009) 184 [arXiv:0812.4432] [SPIRES].
J. Mas, J.P. Shock and J. Tarrio, Holographic Spectral Functions in Metallic AdS/CFT, JHEP 09 (2009) 032 [arXiv:0904.3905] [SPIRES].
A. Karch, A. O’Bannon and E. Thompson, The Stress-Energy Tensor of Flavor Fields from AdS/CFT, JHEP 04 (2009) 021 [arXiv:0812.3629] [SPIRES].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [SPIRES].
J. McGreevy, Holographic duality with a view toward many-body physics, arXiv:0909.0518 [SPIRES].
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Ammon, M., Hoyos, C., O’Bannon, A. et al. Holographic flavor transport in Schrödinger spacetime. J. High Energ. Phys. 2010, 12 (2010). https://doi.org/10.1007/JHEP06(2010)012
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DOI: https://doi.org/10.1007/JHEP06(2010)012