  We discuss transport and localization properties on the insulating side of
the disorder dominated superconductor-insulator transition, described in terms
of the dirty boson model. Analyzing the spectral properties of the interacting
bosons in the absence of phonons, we argue that the Bose glass phase admits
three distinct regimes. For strongest disorder the boson system is a fully
localized, perfect insulator at any temperature. At smaller disorder, only the
low temperature phase exhibits perfect insulation while delocalization takes
place above a finite temperature. We argue that a third phase must intervene
between these perfect insulators and the superconductor. This conducting Bose
glass phase is characterized by a mobility edge in the many body spectrum,
located at finite energy above the ground state. In this insulating regime
purely electronically activated transport occurs, with a conductivity following
an Arrhenius law at asymptotically low temperatures, while a tendency to
superactivation is predicted at higher T. These predictions are in good
agreement with recent transport experiments in highly disordered films of
superconducting materials.
