On the permanence of renormalons in compactified spaces

TL;DR

This paper studies how renormalon singularities behave under spatial compactifications in a scalar field theory, finding that the number and position of poles are unaffected by compactification size or dimensions, only their residues change.

Contribution

It demonstrates that compactification size and dimensions do not alter the number or location of renormalon poles, only their residues, highlighting the robustness of renormalon structure under compactification.

Findings

Number and location of renormalon poles are unaffected by compactification.

Residues of renormalon poles depend on the size of the compactified dimensions.

Careful checks are needed when analyzing asymptotic approximations in this context.

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.