Abstract
We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength deformations of solutions generated by the symmetry. By computing the boundary theory retarded Green’s function we show the existence of a gapless mode with a diffusive dispersion relation. The diffusive character of the mode is compatible with the absence of a conserved charge from the field theory point of view. We give an analytic expression for the corresponding diffusion constant in terms of thermodynamic data and a new transport coefficient σb which is fixed by the black hole horizon data. After adding a perturbative source on the boundary, we compute the resulting gap δωg as a simple function of σb and of data of the thermal state.
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References
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys.A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav.26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [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, Holographic Superconductors, JHEP12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev.D 80 (2009) 105007 [arXiv:0908.1972] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev.D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, arXiv:1810.05338 [INSPIRE].
D. Anninos, S.A. Hartnoll and N. Iqbal, Holography and the Coleman-Mermin-Wagner theorem, Phys. Rev.D 82 (2010) 066008 [arXiv:1005.1973] [INSPIRE].
A. Donos and C. Pantelidou, Holographic transport and density waves, JHEP05 (2019) 079 [arXiv:1903.05114] [INSPIRE].
A. Donos, D. Martin, C. Pantelidou and V. Ziogas, Incoherent hydrodynamics and density waves, arXiv:1906.03132 [INSPIRE].
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, Diffusion and universal relaxation of holographic phonons, arXiv:1904.11445 [INSPIRE].
R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP10 (2015) 112 [arXiv:1507.07137] [INSPIRE].
L. Alberte, M. Ammon, A. Jiménez-Alba, M. Baggioli and O. Pujolàs, Holographic Phonons, Phys. Rev. Lett.120 (2018) 171602 [arXiv:1711.03100] [INSPIRE].
L. Alberte, M. Ammon, M. Baggioli, A. Jiménez and O. Pujolàs, Black hole elasticity and gapped transverse phonons in holography, JHEP01 (2018) 129 [arXiv:1708.08477] [INSPIRE].
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, A holographic strange metal with slowly fluctuating translational order, arXiv:1812.08118 [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav.19 (2002) 5849 [hep-th/0209067] [INSPIRE].
I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP08 (2005) 004 [hep-th/0505190] [INSPIRE].
A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion for Holographic Lattices, JHEP03 (2018) 056 [arXiv:1710.04221] [INSPIRE].
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev.D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP01 (2012) 061 [arXiv:1109.0471] [INSPIRE].
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys.11 (2015) 54 [arXiv:1405.3651] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion in inhomogeneous media, Phys. Rev.D 96 (2017) 125003 [arXiv:1708.05412] [INSPIRE].
K.B. Lyons, R.N. Bhatt, T.J. Negran and H.J. Guggenheim, Incommensurate structural phase transition in bamnf4: Light scattering from phasons, Phys. Rev.B 25 (1982) 1791.
R. Zeyher and W. Finger, Phason dynamics of incommensurate crystals, Phys. Rev. Lett.49 (1982) 1833.
S. Grozdanov, A. Lucas, S. Sachdev and K. Schalm, Absence of disorder-driven metal-insulator transitions in simple holographic models, Phys. Rev. Lett.115 (2015) 221601 [arXiv:1507.00003] [INSPIRE].
M. Blake, Universal Diffusion in Incoherent Black Holes, Phys. Rev.D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE].
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ArXiv ePrint: 1905.00398
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Donos, A., Martin, D., Pantelidou, C. et al. Hydrodynamics of broken global symmetries in the bulk. J. High Energ. Phys. 2019, 218 (2019). https://doi.org/10.1007/JHEP10(2019)218
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DOI: https://doi.org/10.1007/JHEP10(2019)218