Effective Field Theory with a Variable Ultraviolet Cutoff

TL;DR

This paper explores a novel approach to effective field theory by linking ultraviolet and infrared cutoffs, deriving an exact flow equation within the Wilsonian renormalization group framework, impacting our understanding of fixed points and coupling behaviors.

Contribution

It introduces a method to incorporate a variable ultraviolet cutoff into effective field theory using the Wilsonian renormalization group, providing new insights into the flow of couplings and fixed points.

Findings

Derived an exact flow equation for the effective action.

Discussed implications for infrared fixed points.

Explored the running of couplings with a variable cutoff.

Abstract

The properties of strongly gravitating systems suggest that field theory overcounts the states of a system. Reducing the number of degrees of freedom, without abandoning the notion of effective field theory, may be achieved through a connection between the ultraviolet and infrared cutoffs. We provide an implementation of this idea within the Wilsonian approach to the renormalization group. We derive an exact flow equation that describes the evolution of the effective action. We discuss the implications for the existence of infrared fixed points and the running of couplings. We also give an alternative derivation in the context of the perturbative renormalization group.