Global Defects in Field Theory with Applications to Condensed Matter

TL;DR

This paper reviews the theory of global defects in scalar field systems across various dimensions, providing methods to find solutions and illustrating applications in condensed matter physics.

Contribution

It introduces a systematic approach to identify stable global defects in scalar field models for any dimension and demonstrates solving higher-dimensional problems via one-dimensional soluble models.

Findings

Stable global defects exist in models with specific potentials across dimensions

First-order differential equations simplify solving defect configurations

Applications span condensed matter physics and other fields

Abstract

We review investigations on defects in systems described by real scalar fields in (D,1) space-time dimensions. We first work in one spatial dimension, with models described by one and two real scalar fields, and in higher dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D=1. We illustrate the procedure examining specific models and showing how they may be used in applications in different contexts in condensed matter physics, and in other areas.