# On the Universality of Certain Non-Renormalizable Contributions in Two-Dimensional Quantum Field Theory

## TL;DR

This paper investigates the removal of ultraviolet cutoffs in a 2D quantum field theory with non-renormalizable interactions, showing that finite parts can be separated and are independent of regularization schemes, relevant for physical interface models.

## Contribution

It demonstrates that even with non-renormalizable interactions, the finite contributions in 2D QFT can be isolated and are scheme-independent, extending understanding of such models.

## Key findings

- Finite and divergent parts can be separated in non-renormalizable 2D QFT.
- Finite part is independent of regularization scheme.
- Applicable to models describing finite size effects of interfaces.

## Abstract

We consider the question of removing the ultraviolet cutoff in a 2D Quantum Field Theory with an interaction term which is non-renormalizable by power counting. This model arises as the first non-trivial 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 non-renormalizable, 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.