Renormalization and quantum effects in a two-dimensional planar model

We examine the influence of the charging energy on the vortex unbinding transition in two-dimensional arrays of Josephson junctions. The fluctuations of the phase about the time-dependent vortex solutions are treated within the self-consistent harmonic approximation. A new relation between the renormalized vortex unbinding temperature T_c and the charging energy U is derived. We predict a continuous drop of T_c at a critical value of U well below the spurious first order transition of the rigidity constant. The results are interpreted as a quantum assisted dissociation of vortex pairs.