Weakly localized bosons

In this paper, we argue that, in two dimensions, the weak localization of bosons, which occurs on the insulating side of the superconductor-insulator transition, is characterized by $\ensuremath{\rho}\ensuremath{\sim}\mathrm{ln}(1/T),$ as compared to $\ensuremath{\sigma}\ensuremath{\sim}\mathrm{ln}T$ for fermions. This unconventional behavior is tied to the diffusion pole of the delocalized (uncondensed) vortices.