Abstract
The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time correlation functions of scaling operators in the generalised quantum Lifshitz model are given by a d-dimensional higher-derivative conformal field theory. Autocorrelation functions in the generalised quantum Lifshitz model in any number of dimensions can on the other hand be expressed in terms of autocorrelation functions of a two-dimensional conformal field theory. This also holds for autocorrelation functions in a strongly coupled Lifshitz field theory with a holographic dual of Einstein-Maxwell-dilaton type. The map to a two-dimensional conformal field theory extends to autocorrelation functions in thermal states and out-of-equilbrium states preserving symmetry under spatial translations and rotations in both types of Lifshitz models. Furthermore, the spectrum of quasinormal modes of scalar field perturbations in Lifshitz black hole backgrounds can be obtained analytically at low spatial momenta and exhibits a linear dispersion relation at z = d. At high momentum, the mode spectrum can be obtained in a WKB approximation and displays very different behaviour compared to holographic duals of conformal field theories. This has implications for thermalisation in strongly coupled Lifshitz field theories with z > 1.
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References
E. Ardonne, P. Fendley and E. Fradkin, Topological order and conformal quantum critical points, Annals Phys. 310 (2004) 493 [cond-mat/0311466] [INSPIRE].
C. Brust and K. Hinterbichler, Free □k scalar conformal field theory, JHEP 02 (2017) 066 [arXiv:1607.07439] [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].
P. Koroteev and M. Libanov, On existence of self-tuning solutions in static braneworlds without singularities, JHEP 02 (2008) 104 [arXiv:0712.1136] [INSPIRE].
P. Ghaemi, A. Vishwanath and T. Senthil, Finite-temperature properties of quantum Lifshitz transitions between valence-bond solid phases: an example of local quantum criticality, Phys. Rev. B 72 (2005) 024420 [cond-mat/0412409].
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].
V. Keranen, E. Keski-Vakkuri and L. Thorlacius, Thermalization and entanglement following a non-relativistic holographic quench, Phys. Rev. D 85 (2012) 026005 [arXiv:1110.5035] [INSPIRE].
V. Balasubramanian et al., Thermalization of the spectral function in strongly coupled two dimensional conformal field theories, JHEP 04 (2013) 069 [arXiv:1212.6066] [INSPIRE].
J.B. Hartle and S.W. Hawking, Path integral derivation of black hole radiance, Phys. Rev. D 13 (1976) 2188 [INSPIRE].
V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].
G. Festuccia and H. Liu, Excursions beyond the horizon: black hole singularities in Yang-Mills theories. I, JHEP 04 (2006) 044 [hep-th/0506202] [INSPIRE].
T. Andrade and S.F. Ross, Boundary conditions for scalars in Lifshitz, Class. Quant. Grav. 30 (2013) 065009 [arXiv:1212.2572] [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].
W. Sybesma and S. Vandoren, Lifshitz quasinormal modes and relaxation from holography, JHEP 05 (2015) 021 [arXiv:1503.07457] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
G. Festuccia and H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, Adv. Sci. Lett. 2 (2009) 221 [arXiv:0811.1033] [INSPIRE].
U. Gürsoy, A. Jansen, W. Sybesma and S. Vandoren, Holographic equilibration of nonrelativistic plasmas, Phys. Rev. Lett. 117 (2016) 051601 [arXiv:1602.01375] [INSPIRE].
V. Keranen and L. Thorlacius, Thermal correlators in holographic models with Lifshitz scaling, Class. Quant. Grav. 29 (2012) 194009 [arXiv:1204.0360] [INSPIRE].
A. Jansen, Mathematica package QNMspectral, http://www.uu.nl/staff/APJansen#tabOnderzoek.
M. Abramowitz and I. Stegun, Handbook of mathematical functions, Dover Publications, New York U.S.A., (1965).
J.F. Fuini, C.F. Uhlemann and L.G. Yaffe, Damping of hard excitations in strongly coupled N = 4 plasma, JHEP 12 (2016) 042 [arXiv:1610.03491] [INSPIRE].
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ArXiv ePrint: 1611.09371
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Keränen, V., Sybesma, W., Szepietowski, P. et al. Correlation functions in theories with Lifshitz scaling. J. High Energ. Phys. 2017, 33 (2017). https://doi.org/10.1007/JHEP05(2017)033
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DOI: https://doi.org/10.1007/JHEP05(2017)033