String Representation of the Abelian Higgs Theory and Aharonov-Bohm Effect on the Lattice

TL;DR

This paper reformulates the 4D lattice Abelian Higgs theory using string world sheets, revealing a topological long-range interaction between strings and particles related to their linking number.

Contribution

It introduces a string representation of the Abelian Higgs theory on the lattice and demonstrates the existence of topological long-range interactions.

Findings

Partition function expressed as sum over Nielsen--Olesen string world sheets

Construction of string creation and annihilation operators

Identification of topological long-range interactions proportional to linking number

Abstract

The partition function of the $4D$ lattice Abelian Higgs theory is represented as the sum over world sheets of Nielsen--Olesen strings. The creation and annihilation operators of the strings are constructed. The topological long--range interaction of the strings and charged particles is shown to exist; it is proportional to the linking number of the string world sheet and particle world trajectory.