Dimensional regularization of a compact dimension

TL;DR

This paper introduces a dimensional regularization method tailored for compact dimensions, maintaining the Kaluza-Klein structure and simplifying the identification of divergences and finite parts in one-loop Feynman graphs.

Contribution

It presents a novel regularization scheme for compact dimensions that preserves the Kaluza-Klein tower and facilitates divergence analysis.

Findings

Preserves Kaluza-Klein tower structure.

Eases identification of divergences and finite parts.

Applicable to one-loop Feynman graphs in compact dimensions.

Abstract

An extension of dimensional regularization to the case of compact dimensions is presented. The procedure preserves the Kaluza-Klein tower structure, but has a regulator specific to the compact dimension. Possible 5 and 4 dimensional divergent as well as manifest finite contributions of (one-loop) Feynman graphs can easily be identified in this scheme.