On dimensional regularization of sums

TL;DR

This paper presents a systematic dimensional regularization method for divergent sums in field theories with compact dimensions or finite temperature, maintaining symmetries and separating divergences from finite terms.

Contribution

It introduces a regularization technique that preserves symmetries and simplifies the separation of divergences from finite contributions in theories with compactified dimensions.

Findings

The method effectively regularizes divergent sums in compactified field theories.

It maintains the symmetries of the original action during regularization.

The approach clearly separates divergences from finite, radius-dependent terms.

Abstract

We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the conventional dimensional regularization and allows an easy separation of the regulated divergence from the finite term that depends on the compactification radius (temperature).