Holographic zero sound from spacetime-filling branes

Nikola Gushterov (Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Department of Physics, Clarendon Laboratory, Oxford, OX1 3NU, U.K.) ; Andy O’Bannon (STAG Research Centre, Physics and Astronomy, University of Southampton Highfield, Southampton, SO17 1BJ, U.K.) ; Ronnie Rodgers (STAG Research Centre, Physics and Astronomy, University of Southampton Highfield, Southampton, SO17 1BJ, U.K.)

We use holography to study sound modes of strongly-interacting conformal field theories with non-zero temperature, T , and U(1) chemical potential, μ. Specifically, we consider charged black brane solutions of Einstein gravity in (3+1)-dimensional Anti-de Sitter space coupled to a U(1) gauge field with Dirac-Born-Infeld action, representing a spacetime-filling brane. The brane action has two free parameters: the tension and the non-linearity parameter, which controls higher-order terms in the field strength. For all values of the tension, non-linearity parameter, and T /μ, and at sufficiently small momentum, we find sound modes with speed given by the conformal value and attenuation constant of hydrodynamic form. In particular we find sound at arbitrarily low T /μ, outside the usual hydrodynamic regime, but in the regime where a Fermi liquid exhibits Landau’s “zero” sound. In fact, the sound attenuation constant as a function of T /μ qualitatively resembles that of a Fermi liquid, including a maximum, which in a Fermi liquid signals the collisionless to hydrodynamic crossover. We also explore regimes of the tension and non-linearity parameter where two other proposed definitions of the crossover are viable, via pole collisions in Green’s functions or peak movement in the charge density spectral function.

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      "surname": "O\u2019Bannon", 
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      "value": "We use holography to study sound modes of strongly-interacting conformal field theories with non-zero temperature, T , and U(1) chemical potential, \u03bc. Specifically, we consider charged black brane solutions of Einstein gravity in (3+1)-dimensional Anti-de Sitter space coupled to a U(1) gauge field with Dirac-Born-Infeld action, representing a spacetime-filling brane. The brane action has two free parameters: the tension and the non-linearity parameter, which controls higher-order terms in the field strength. For all values of the tension, non-linearity parameter, and T /\u03bc, and at sufficiently small momentum, we find sound modes with speed given by the conformal value and attenuation constant of hydrodynamic form. In particular we find sound at arbitrarily low T /\u03bc, outside the usual hydrodynamic regime, but in the regime where a Fermi liquid exhibits Landau\u2019s \u201czero\u201d sound. In fact, the sound attenuation constant as a function of T /\u03bc qualitatively resembles that of a Fermi liquid, including a maximum, which in a Fermi liquid signals the collisionless to hydrodynamic crossover. We also explore regimes of the tension and non-linearity parameter where two other proposed definitions of the crossover are viable, via pole collisions in Green\u2019s functions or peak movement in the charge density spectral function."
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Published on:
11 October 2018
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2018 (2018)
Issue 10
Pages 1-58
DOI:
https://doi.org/10.1007/JHEP10(2018)076
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: