Quantum Theory of Strings in Abelian Higgs Model

TL;DR

This paper develops a quantum theory for Abrikosov--Nielsen--Olesen strings within the Abelian Higgs model, demonstrating the absence of conformal anomaly in four dimensions and exploring topological effects like the Aharonov--Bohm phenomenon.

Contribution

It constructs the quantum string theory from the Abelian Higgs model, analyzing anomalies, topological interactions, and explicit creation operators.

Findings

Quantum theory of strings is consistent in four dimensions.

Aharonov--Bohm effect induces nontrivial commutation relations.

Creation operators are explicitly constructed in both path integral and Hamiltonian form.

Abstract

Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space -- time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent, and the quantum theory exists. We also study an analogue of the Aharonov--Bohm effect: the corresponding topological interaction is proportional to the linking number of the string world sheet and the particle world trajectory. The creation operators of the strings are explicitly constructed in the path integral and in the Hamiltonian formulation of the theory. We show that the Aharonov--Bohm effect gives rise to several nontrivial commutation relations.