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arXiv · 1905.00398

Hydrodynamics of broken global symmetries in the bulk

Aristomenis Donos·Daniel Martin·Christiana Pantelidou·Vaios Ziogas
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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 $σ_{b}$ which is fixed by the black hole horizon data. After adding a perturbative source on the boundary, we compute the resulting gap $δω_{g}$ as a simple function of $σ_{b}$ and of data of the thermal state.

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Aristomenis Donos, Daniel Martin, Christiana Pantelidou, Vaios Ziogas. 2019-10-28. Hydrodynamics of broken global symmetries in the bulk. https://doi.org/10.1007/jhep10(2019)218

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