Short strings in the Abelian Higgs model

We consider the monopole-antimonopole static potential in the confining pha se of the Abelian Higgs model and in particular the corrections to the Coul omb-like potential at small distances r. By minimizing numerically the clas sical 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 connec ted by a mathematically thin line along which the scalar field vanishes. Th ese short strings modify the operator product expansion as well. Implicatio ns for QCD are discussed.