We consider the question of removing the ultraviolet cutoff in a 2D quantum field theory with an interaction term which is nonrenormalizable by power counting. This model arises as the first nontrivial correction beyond the Gaussian approximation of the so-called capillary wave or drumhead model, and is rather important from a physical point of view since it correctly describes the finite size effects of two-dimensional interfaces. Despite the fact that the interaction is nonrenormalizable, we prove that for a large class of regularization schemes the finite and divergent parts can be separated in a simple way. Furthermore, the finite part is independent of the choice of cutoff prescription used.

• Received 29 February 1996

DOI:https://doi.org/10.1103/PhysRevD.54.5179