Simulation of an Abelian Higgs theory in world line (polymer) representation

In World Line Path Integral representation Abelian Higgs theories admit a curvature term in the Hamiltonian. Using Monte Carlo simulations we show that the curvature term drives a phase transition at sufficiently strong coupling. In quenched approximation this phase transition is smooth, with implications that the model reduces to a Goldstone theory. Critical properties of the system near the transition are investigated and found to be consistent with mean field behavior.