  We study the long-time aging dynamics of spin-glass models with two-spin
interactions by performing a Renormalization Group transformation on the time
variable in the non-equilibrium dynamical generating functional. We obtain the
RG equations and find that the flow converges to an exact fixed point. We show
that this fixed point is invariant under reparametrizations of the time
variable. This continuous symmetry is broken, as evidenced by the fact that the
observed correlations and responses are not invariant under it. We argue that
this gives rise to the presence of Goldstone modes, and that those Goldstone
modes shape the behavior of fluctuations in the nonequilibrium dynamics.
