Abstract
We obtain relaxation times for field theories with Lifshitz scaling and with holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by computing quasinormal modes of a bulk scalar field in the presence of Lifshitz black branes. We determine the relation between relaxation time and dynamical exponent z, for various values of boundary dimension d and operator scaling dimension. It is found that for d > z + 1, at zero momenta, the modes are underdamped, where as for d ≤ z + 1 the system is always overdamped. For d = z + 1 and zero momenta, we present analytical results.
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References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [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].
K. Balasubramanian and J. McGreevy, An Analytic Lifshitz black hole, Phys. Rev. D 80 (2009) 104039 [arXiv:0909.0263] [INSPIRE].
D.T. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schr¨odinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
J. Tarrio and S. Vandoren, Black holes and black branes in Lifshitz spacetimes, JHEP 09 (2011) 017 [arXiv:1105.6335] [INSPIRE].
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [INSPIRE].
Y.S. Myung and T. Moon, Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes, Phys. Rev. D 86 (2012) 024006 [arXiv:1204.2116] [INSPIRE].
E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: From astrophysics to string theory, Rev. Mod. Phys. 83 (2011) 793 [arXiv:1102.4014] [INSPIRE].
B. Cuadros-Melgar, J. de Oliveira and C.E. Pellicer, Stability Analysis and Area Spectrum of 3-Dimensional Lifshitz Black Holes, Phys. Rev. D 85 (2012) 024014 [arXiv:1110.4856] [INSPIRE].
E. Abdalla, O.P.F. Piedra, F.S. Nuñez and J. de Oliveira, Scalar field propagation in higher dimensional black holes at a Lifshitz point, Phys. Rev. D 88 (2013) 064035 [arXiv:1211.3390] [INSPIRE].
A. Giacomini, G. Giribet, M. Leston, J. Oliva and S. Ray, Scalar field perturbations in asymptotically Lifshitz black holes, Phys. Rev. D 85 (2012) 124001 [arXiv:1203.0582] [INSPIRE].
P.A. Gonzalez, J. Saavedra and Y. Vasquez, Quasinormal modes and Stability Analysis for 4-dimensional Lifshitz Black Hole, Int. J. Mod. Phys. D 21 (2012) 1250054 [arXiv:1201.4521] [INSPIRE].
P.A. Gonzalez, F. Moncada and Y. Vasquez, Quasinormal Modes, Stability Analysis and Absorption Cross Section for 4-dimensional Topological Lifshitz Black Hole, Eur. Phys. J. C 72 (2012) 2255 [arXiv:1205.0582] [INSPIRE].
R.B. Mann, Lifshitz Topological Black Holes, JHEP 06 (2009) 075 [arXiv:0905.1136] [INSPIRE].
E.J. Brynjolfsson, U.H. Danielsson, L. Thorlacius and T. Zingg, Holographic Superconductors with Lifshitz Scaling, J. Phys. A 43 (2010) 065401 [arXiv:0908.2611] [INSPIRE].
T. Andrade and S.F. Ross, Boundary conditions for scalars in Lifshitz, Class. Quant. Grav. 30 (2013) 065009 [arXiv:1212.2572] [INSPIRE].
M. Abramowitz and I.A. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, Applied Mathematics Series (Book 55), Courier Dover Publications (1972).
H.T. Cho, A.S. Cornell, J. Doukas, T.R. Huang and W. Naylor, A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method, Adv. Math. Phys. 2012 (2012) 281705 [arXiv:1111.5024] [INSPIRE].
H. Ciftci, R.L. Hall and N. Saad, Asymptotic iteration method for eigenvalue problems, J. Phys. Math. Gen. 36 (2003) 11807.
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Sybesma, W., Vandoren, S. Lifshitz quasinormal modes and relaxation from holography. J. High Energ. Phys. 2015, 21 (2015). https://doi.org/10.1007/JHEP05(2015)021
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DOI: https://doi.org/10.1007/JHEP05(2015)021