Abstract
We explore the momentum analyticity of the static transverse polarization tensor of a 2+1 dimensional holographic superconductor in its normal phase, aiming at finding the holographic counterpart of the singularities underlying the Friedel oscillations of an ordinary field theory. We prove that the polarization tensor is a meromorphic function with an infinite number of poles located on the complex momentum plane off real axis. With the aid of the WKB approximation these poles are found to lies asymptotically along two straight lines parallel to the imaginary axis for a large momentum magnitude. The similarity between the holographic Green’s function and that of an weakly coupled ordinary field theory (e.g., 2+1 dimensional QED) regarding the location of the momentum singularities offers further support to the validity of the gauge/gravity duality.
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References
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [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. 2. Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [INSPIRE].
D.-F. Hou, J.-R. Li, H. Liu and H.-C. Ren, The momentum analyticity of two-point correlators from perturbation theory and AdS/CFT, JHEP 07 (2010) 042 [arXiv:1003.5462] [INSPIRE].
W. Kohn and J.M. Luttinger, New Mechanism for Superconductivity, Phys. Rev. Lett. 15 (1965) 63.
V. Galitski and S. Das Sarma, Kohn-Luttinger pseudopairing in a two-dimensional Fermi liquid, Phys. Rev. B 67 (2003) 144520 [cond-mat/0211355].
R. Egger and H. Grabert, Friedel oscillations for interacting fermions in one dimension, [cond-mat/9509100].
M. Blake, A. Donos and D. Tong, Holographic charge oscillations, JHEP 04 (2015) 019 [arXiv:1412.2003] [INSPIRE].
M. Edalati, J.I. Jottar and R.G. Leigh, Shear modes, criticality and extremal black holes, JHEP 04 (2010) 075 [arXiv:1001.0779] [INSPIRE].
H. Kodama and A. Ishibashi, Master equations for perturbations of generalized static black holes with charge in higher dimensions, Prog. Theor. Phys. 111 (2004) 29 [hep-th/0308128] [INSPIRE].
L. Yin, H.C. Ren, T.K. Lee and D.F. Hou, Momentum analyticity of the electric polarizability of a holographic QED 3, work in progress.
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ArXiv ePrint: 1605.07547
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Yin, L., Ren, Hc., Lee, T.K. et al. Momentum analyticity of transverse polarization tensor in the normal phase of a holographic superconductor. J. High Energ. Phys. 2016, 116 (2016). https://doi.org/10.1007/JHEP08(2016)116
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DOI: https://doi.org/10.1007/JHEP08(2016)116