Hydrodynamics of broken global symmetries in the bulk
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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.
KeywordsGauge-gravity correspondence Holography and condensed matter physics (AdS/CMT)
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