Field theory of statics and dynamics of glasses: Rare events and barrier distributions

We study thermally activated dynamics rising functional renormalization within the field theory of randomly pinned elastic systems, a prototype for glasses. It appears through an essentially non-perturbative boundary layer in the running effective action, for which we find a consistent scaling ansatz to all orders. We find that in the statics the boundary layer describes the physics of rare low-energy metastable states as suggested by a phenomenological droplet picture. The extension to equilibrium dynamics mandates a non-trivial broad distribution of relaxation tunes for the large-scale anodes; hitherto neglected in analytic calculations.