Quantum Global Strings and Their Correlation Functions

TL;DR

This paper provides a comprehensive quantum description of global vortex strings in a Higgs system with broken U(1) symmetry, including explicit operators and correlation functions relevant for cosmology and condensed matter.

Contribution

It introduces an explicit string creation operator and evaluates the quantum string correlation function within a dual Higgs framework.

Findings

Derived an explicit string creation operator in Higgs and dual formulations.

Computed the quantum string correlation function.

Obtained the string energy density from correlation functions.

Abstract

A full quantum description of global vortex strings is presented in the framework of a pure Higgs system with a broken global U(1) symmetry in 3+1D. An explicit expression for the string creation operator is obtained, both in terms of the Higgs field and in the dual formulation where a Kalb-Ramond antisymmetric tensor gauge field is employed as the basic field. The quantum string correlation function is evaluated and from this, the string energy density is obtained. Potential application in cosmology (cosmic strings) and condensed matter (vortices in superfluids) are discussed.