Interaction between vortices in models with two order parameters

TL;DR

This paper analyzes how the interaction energy and force between distant strings are affected in a field theory with two order parameters, relevant to superconducting cosmic strings, high-temperature superconductivity, and nonlinear optics.

Contribution

It introduces the impact of a second order parameter, possibly broken in the string core, on the energetics of widely separated strings in models with two order parameters.

Findings

Second order parameter's breaking in the core influences string interactions.

Longer length scale of the second order parameter amplifies its effect.

Interaction energy depends on the behavior of both order parameters.

Abstract

The interaction energy and force between widely separated strings is analyzed in a field theory having applications to superconducting cosmic strings, the SO(5) model of high-temperature superconductivity, and solitons in nonlinear optics. The field theory has two order parameters, one of which is broken in the vacuum (giving rise to strings), the other of which is unbroken in the vacuum but which could nonetheless be broken in the core of the string. If this does occur, there is an effect on the energetics of widely separated strings. This effect is important if the length scale of this second order parameter is longer than that of the other fields in the problem.