Renormalized Kaluza-Klein theories

TL;DR

This paper investigates the one-loop renormalization of six-dimensional QED and demonstrates that the four-dimensional effective theory retains memory of its higher-dimensional origin, with precise determination of counterterms.

Contribution

It provides a detailed analysis of how higher-dimensional renormalization effects influence the four-dimensional effective theory, establishing a clear connection between the two.

Findings

Four-dimensional theory retains higher-dimensional information after renormalization.

Counterterms in 4D are precisely determined by 6D origin.

Reduction of QED4 on a two-torus confirms the results.

Abstract

Using six-dimensional quantum electrodynamics ($QED_6$) as an example we study the one-loop renormalization of the theory both from the six and four-dimensional points of view. Our main conclusion is that the properly renormalized four dimensional theory never forgets its higher dimensional origin. In particular, the coefficients of the neccessary extra counterterms in the four dimensional theory are determined in a precise way. We check our results by studying the reduction of $QED_4$ on a two-torus.