New Type of String Solutions with Long Range Forces

TL;DR

This paper investigates a novel string solution in a two-scalar-field Abelian Higgs model, revealing unique long-range force effects and confirming their formation through lattice simulations.

Contribution

It introduces the uncompensated string, a new type of solution with global string-like divergence, and explores their dynamics and formation in a two-scalar-field model.

Findings

Discovery of the uncompensated string with logarithmic divergence.

Confirmation of string formation via lattice simulations.

Evolution of uncompensated strings into local strings over time.

Abstract

We explore the formation and the evolution of the string network in the Abelian Higgs model with two complex scalar fields. A special feature of the model is that it possesses a global $U(1)$ symmetry in addition to the $U(1)$ gauge symmetry. Both symmetries are spontaneously broken by the vacuum expectation values of the two complex scalar fields. As we will show the dynamics of the string network is quite rich compared with that in the ordinary Abelian Higgs model with a single complex scalar field. In particular, we find a new type of string solutions in addition to the conventional Abrikosov-Nielsen-Olesen (local) string solution. We call this the uncompensated string. An isolated uncompensated string has a logarithmic divergent string tension as in the case of the global strings, although it is accompanied by a non-trivial gauge field configuration. We also perform classical lattice simulations in the $2+1$ dimensional spacetime, which confirms the formation of the uncompensated strings at the phase transition. We also find that most of the uncompensated strings evolve into the local strings at later time when the gauge charge of the scalar field with a smaller vacuum expectation value is larger than that of the scalar field with a larger vacuum expectation value.