Exact Scheme Independence

TL;DR

This paper demonstrates that scheme independence in exact renormalization group equations stems from general field redefinitions, leading to a covariant formulation where the kernel acts as a field connection, highlighting inherent redundancies.

Contribution

It shows that scheme independence arises from field redefinitions and introduces a covariant formulation where the kernel functions as a field connection along the flow.

Findings

Scheme independence follows from field redefinitions.

The RG equations are covariant under a symmetry group.

The kernel acts as a field connection along the flow.

Abstract

Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories. Renormalization group equations and their solutions are amenable to a simple formulation which is manifestly covariant under such a symmetry group. Notably, the kernel of the exact equations which controls the integration of modes acts as a field connection along the flow.