Abstract
We study the lattice effects on the simple holographic toy model; massive U(1) gauge theory for the bulk action. The mass term is for the U(1) gauge symmetry breaking in the bulk. Without the lattice, the AC conductivity of this model shows similar results to the holographic superconductor with the energy gap. On this model, we introduce the lattice effects, which induce the periodic potential and break the translational invariance of the boundary field theory. Without the lattice, due to the translational invariance and the mass term, there is a delta function peak at zero frequency on the AC conductivity. We study how this delta function peak is influenced by the lattice effects, which we introduce perturbatively. In the probe limit, we evaluate the perturbative corrections to the conductivities at very small frequency limit. We find that the delta function peak remains, even after the lattice effects are introduced, although its weight reduces perturbatively. We also study the lattice wavenumber dependence of this weight. Our result suggests that in the U(1) symmetry breaking phase, the delta function peak is stable against the lattice effects at least perturbatively.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
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].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].
S. Sachdev, Condensed matter and AdS/CFT, arXiv:1002.2947 [INSPIRE].
S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [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].
C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
G.T. Horowitz, Introduction to holographic superconductors, arXiv:1002.1722 [INSPIRE].
K. Goldstein et al., Holography of dyonic dilaton black branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].
K. Maeda and T. Okamura, Vortex flow for a holographic superconductor, Phys. Rev. D 83 (2011) 066004 [arXiv:1012.0202] [INSPIRE].
K. Maeda, T. Okamura and J.-i. Koga, Inhomogeneous charged black hole solutions in asymptotically Anti-de Sitter spacetime, Phys. Rev. D 85 (2012) 066003 [arXiv:1107.3677] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Lattice potentials and fermions in holographic non Fermi-liquids: hybridizing local quantum criticality, JHEP 10 (2012) 036 [arXiv:1205.5227] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1207.2943
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Iizuka, N., Maeda, K. Towards the lattice effects on the holographic superconductor. J. High Energ. Phys. 2012, 117 (2012). https://doi.org/10.1007/JHEP11(2012)117
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2012)117