Compactification of spatial extra dimensions

[DuckAmuck]

TL;DR

Looking to understand results of a paper.

Hi everyone,
I am looking at a paper on compact dimensions. Equation 65 makes sense except for the term of 4*pi*n*R in the denominator. Why is it 4*pi and not 2*pi? I cannot rationalize this. Please help. Thank you.
https://arxiv.org/ftp/hep-ph/papers/0609/0609260.pdf

 

[Milsomonk]

The Coulomb force law needs to be modified such that $R_n$ takes into account the true separation of charges. The separation in the compactified extra dimension is given by this $4\pi n R$ term which is specific to the Torus geometry. If the extra dimension was compactified on a circle you may well have a factor of $2\pi n R$ as you expected.