Abstract
The absence of fixed momentum excitations in a theory with Lifshitz scale invariance gives rise to exponential suppression of spectral weight in the low-frequency limit. In the holographic dual, this suppression arises as a consequence of a tunneling barrier that decouples the horizon from the boundary. We compute the spin-1/2 holographic Green’s function and show that the form of the barrier is identical to that of the scalar case. We furthermore demonstrate that the suppression factor is universal in the \( \widehat{\omega}\to 0 \) limit where \( \widehat{\omega}=\omega /\left|\overrightarrow{k}\right|{}^{\mathrm{z}} \) . In particular, it depends only on ω and the critical exponent z, and is independent of scaling dimension and spin.
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References
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
K. Copsey and R. Mann, Pathologies in asymptotically Lifshitz spacetimes, JHEP 03 (2011) 039 [arXiv:1011.3502] [INSPIRE].
G.T. Horowitz and B. Way, Lifshitz singularities, Phys. Rev. D 85 (2012) 046008 [arXiv:1111.1243] [INSPIRE].
S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz horizons, JHEP 02 (2014) 085 [arXiv:1202.6635] [INSPIRE].
N. Bao, X. Dong, S. Harrison and E. Silverstein, The Benefits of Stress: Resolution of the Lifshitz Singularity, Phys. Rev. D 86 (2012) 106008 [arXiv:1207.0171] [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].
G. Knodel and J.T. Liu, Higher derivative corrections to Lifshitz backgrounds, JHEP 10 (2013) 002 [arXiv:1305.3279] [INSPIRE].
C. Keeler, G. Knodel and J.T. Liu, What do non-relativistic CFTs tell us about Lifshitz spacetimes?, JHEP 01 (2014) 062 [arXiv:1308.5689] [INSPIRE].
T. Faulkner and J. Polchinski, Semi-holographic Fermi liquids, JHEP 06 (2011) 012 [arXiv:1001.5049] [INSPIRE].
S.A. Hartnoll and E. Shaghoulian, Spectral weight in holographic scaling geometries, JHEP 07 (2012) 078 [arXiv:1203.4236] [INSPIRE].
C. Keeler, G. Knodel and J.T. Liu, Hidden horizons in non-relativistic AdS/CFT, JHEP 08 (2014) 024 [arXiv:1404.4877] [INSPIRE].
S.A. Hartnoll and D.M. Hofman, Locally Critical Resistivities from Umklapp Scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B 431 (1998) 63 [hep-th/9803251] [INSPIRE].
W. Mueck and K.S. Viswanathan, Conformal field theory correlators from classical field theory on anti-de Sitter space. 2. Vector and spinor fields, Phys. Rev. D 58 (1998) 106006 [hep-th/9805145] [INSPIRE].
M. Henneaux, Boundary terms in the AdS/CFT correspondence for spinor fields, hep-th/9902137 [INSPIRE].
N. Iqbal and H. Liu, Real-time response in AdS/CFT with application to spinors, Fortsch. Phys. 57 (2009) 367 [arXiv:0903.2596] [INSPIRE].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [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].
N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity, JHEP 01 (2012) 094 [arXiv:1105.1162] [INSPIRE].
S.A. Hartnoll, D.M. Hofman and D. Vegh, Stellar spectroscopy: fermions and holographic Lifshitz criticality, JHEP 08 (2011) 096 [arXiv:1105.3197] [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Semi-local quantum liquids, JHEP 04 (2012) 086 [arXiv:1105.4621] [INSPIRE].
M. Cubrovic, Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair, Phys. Rev. D 84 (2011) 086002 [arXiv:1106.1798] [INSPIRE].
U. Gürsoy, V. Jacobs, E. Plauschinn, H. Stoof and S. Vandoren, Holographic models for undoped Weyl semimetals, JHEP 04 (2013) 127 [arXiv:1209.2593] [INSPIRE].
M. Alishahiha, M.R. Mohammadi Mozaffar and A. Mollabashi, Fermions on Lifshitz Background, Phys. Rev. D 86 (2012) 026002 [arXiv:1201.1764] [INSPIRE].
L.Q. Fang, X.-H. Ge and X.-M. Kuang, Holographic fermions in charged Lifshitz theory, Phys. Rev. D 86 (2012) 105037 [arXiv:1201.3832] [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.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
P. Basu, Energy scales in a holographic black hole and conductivity at finite momentum, Can. J. Phys. 89 (2011) 271 [arXiv:0911.5082] [INSPIRE].
C. Keeler, G. Knodel, J.T. Liu and K. Sun, Universal features of Lifshitz Green’s functions from holography, JHEP 08 (2015) 057 [arXiv:1505.07830] [INSPIRE].
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
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Kim, Y., Liu, J.T. Holographic Lifshitz fermions and exponentially suppressed spectral weight. J. High Energ. Phys. 2016, 117 (2016). https://doi.org/10.1007/JHEP07(2016)117
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DOI: https://doi.org/10.1007/JHEP07(2016)117