On the permanence of renormalons in compactified spaces

Abstract

We investigate the existence and behavior of renormalon singularities with respect to $d$ spatial compactifications and quasiperiodic boundary conditions. Employing a toy model (scalar field theory with quartic interaction) we find that the size of the compactification and the number of compactified dimensions do not influence the number and the location of the renormalon poles. The only influence occurs in the residues. We enforce the need to carefully check the asymptotic approximations every time there is some result about the appearance of new renormalon poles or their cancellation.