A Perspective on Regularization and Curvature

TL;DR

This paper explores the geometric relationship between regularization schemes and their beta functions using a global connection on a renormalization bundle, linking gauge transformations and solutions over curved spacetime.

Contribution

It introduces a geometric framework connecting regularization schemes and beta functions via a global connection on the renormalization bundle, providing new insights into their structure.

Findings

Global connection relates beta functions across regularization schemes.

Gauge transformations connect different beta functions.

Local solutions to beta functions are characterized over curved spacetime.

Abstract

A global connection on the Connes Marcolli renormalization bundle relates $\beta$-functions of a class of regularization schemes by gauge transformations, as well as local solutions to $\beta$-functions over curved space-time.