Renormalization of the vortex diffusion constant in superfluid films

We study the dynamics of vortices in superfluid helium films, using a phenomenological Langevin equation to account for diffusive as well as convective motion of vortices. We show that in the long-wavelength limit, dynamic screening effects give rise to a renormalization of the diffusion constant, while the convective parameter remains unchanged. The critical behavior is analyzed with renormalization-group methods. In the limit $T\to T_c^{-}$, we find a universal cusp singularity for the diffusion constant, reaching a finite value at $T_c$.