  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 $\sigma_{b}$ which is fixed by the black hole horizon data. After
adding a perturbative source on the boundary, we compute the resulting gap
$\delta\omega_{g}$ as a simple function of $\sigma_{b}$ and of data of the
thermal state.
