Bootstrapping Perturbative Perfect Actions

TL;DR

This paper investigates the perturbative renormalization group of four-dimensional phi4 theory, reformulating it as integral equations to directly define the continuum limit without a bare theory, and proves perturbative renormalizability through scale dimension counting.

Contribution

It introduces a reformulation of the exact renormalization group as integral equations, providing a new perspective on defining the continuum limit and proving renormalizability.

Findings

Integral equations define the continuum limit of phi4 theory.

Proof of perturbative renormalizability via scale dimension counting.

Discussion of universality within the exact renormalization group framework.

Abstract

We study the exact renormalization group of the four dimensional phi4 theory perturbatively. We reformulate the differential renormalization group equations as integral equations that define the continuum limit of the theory directly with no need for a bare theory. We show how the self-consistency of the integral equations leads to the determination of the interaction vertices in the continuum limit. The inductive proof of the existence of a solution to the integral equations amounts to a proof of perturbative renormalizability, and it consists of nothing more than counting the scale dimensions of the interaction vertices. Universality is discussed within a context of the exact renormalization group.