# The Role of Vortex Strings in the Non-Compact Lattice Abelian Higgs Model

## TL;DR

This paper investigates the role of vortex strings in the non-compact lattice Abelian Higgs model, demonstrating how vortex density acts as an order parameter distinguishing different phases.

## Contribution

It introduces a vortex-based representation of the partition function and shows vortex density as a key indicator of phase transitions in the model.

## Key findings

- Vortex density vanishes in the Higgs phase
- Coulomb phase exhibits vortex condensate
- Vortex density serves as an effective order parameter

## Abstract

The non-compact lattice version of the Abelian Higgs model is studied in terms of its topological excitations. The Villain form of the partition function is represented as a sum over world-sheets of gauge-invariant ``vortex'' strings. The phase transition of the system is then related to the density of these excitations. Through Monte Carlo simulations the density of the vortex sheets is shown to be a good order parameter for the system. The vortex density essentially vanishes in the Higgs phase, and the Coulomb phase consists of a single vortex condensate.