Hydrodynamics of broken global symmetries in the bulk

Understand

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.