Short Strings in Abelian Higgs Model

TL;DR

This paper investigates short string corrections to the monopole-antimonopole potential in the Abelian Higgs model, revealing a linear correction at small distances and discussing implications for QCD.

Contribution

It demonstrates the existence of linear stringy corrections at small distances in the Abelian Higgs model and explores their impact on the operator product expansion and QCD.

Findings

Linear correction to potential at small r

Short strings connect monopoles with vanishing scalar field

Implications for operator product expansion and QCD

Abstract

We consider the monopole-antimonopole static potential in the confining phase of the Abelian Higgs model and in particular the corrections to the Coulomb-like potential at small distances r. By minimizing numerically the classical energy functional we observe a linear in r, stringy correction even at distances much smaller than the apparent physical scales. We argue that this term is a manifestation of the condition that the monopoles are connected by a mathematically thin line along which the scalar field vanishes. These short strings modify the operator product expansion as well. Implications for QCD are discussed.