Fermionic String from Abelian Higgs Model with monopoles and $Θ$-term

Abstract

The four dimensional Abelian Higgs model with monopoles and $Θ$-term is considered in the limit of the large mass of the higgs boson. We show that for $Θ=2 π$ the theory is equivalent, at large distances, to summation over all possible world-sheets of fermionic strings with Dirichlet type boundary conditions on string coordinates.