http://www.dartmouth.edu/~dbr/topdefects.pdf

An introduction to topological defects in field theories

Daniel B Reeves

∗

Dept. Physics and Astronomy, Dartmouth College

(Dated: Mar. 7, 2014)

Topology is a relative newcomer to mathematics, but its application to physics has already demon-

strated its likely longevity. In physical field theories, the spaces on which the fields are defined can

be considered manifolds, and if the manifolds have interesting properties, physical insight can be

gleaned from topological considerations. Here we focus on so called ‘topological defects’ or ‘soli-

tons’, topologically stable solutions to field equations, other than the typical vacuum solutions,

that admit new physics. It is the goal of this paper to link the mathematical ideas to the physical

ones, introducing the subject at a level adequate for a first time reader familiar with basic quan-

tum field theory. Thus we aim to connect topological equivalence relations to physical phenomena,

summarizing examples from cosmology as well as condensed matter physics