Topological defects

TL;DR

This survey provides a comprehensive overview of topological defects across various physical theories, including lattice models, quantum field theories, and higher-dimensional contexts, emphasizing their mathematical and physical significance.

Contribution

It systematically reviews the concept of topological defects in multiple theoretical frameworks, highlighting their roles and properties in different dimensions and models.

Findings

Topological defects are fundamental in understanding phase transitions and topological phases.

They appear in lattice models, quantum field theories, and higher-dimensional theories.

The survey connects mathematical structures with physical phenomena involving defects.

Abstract

This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological quantum field theory in arbitrary dimension, and in higher-dimensional quantum field theory with a focus on 4-dimensional quantum electrodynamics.