Unrenormalizable Theories Can Be Predictive

TL;DR

This paper proposes a method to make unrenormalizable theories predictive by fine-tuning to reach the maximal ultraviolet cutoff, enabling unique low-energy predictions despite infinite parameters.

Contribution

It introduces a new approach using the Wilsonian RG and maximal cutoff assumption to extract predictive power from unrenormalizable theories.

Findings

In scalar theories, the method yields unique infrared predictions.

The approach reduces ambiguity in theories with infinite parameters.

Potential application to quantum gravity effective theories.

Abstract

Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence of the maximal ultraviolet cutoff in a cutoff theory, and we require that the theory be so fine-tuned as to reach the maximal cutoff. The theory so obtained behaves as a local continuum theory to the shortest distance. In concrete examples of the scalar theory we find that at least in a certain approximation to the Wilsonian RG, this requirement enable us to make unique predictions in the infrared regime in terms of a finite number of independent parameters. Therefore, the method might provide a way for calculating quantum corrections in a low-energy effective theory of quantum gravity.