Chern-Simons theory in mathematics, condensed matter theory and cosmology

TL;DR

This paper reviews the diverse applications of Chern-Simons theory across mathematics, condensed matter physics, and cosmology, highlighting its role in knot theory, quantum Hall effects, and cosmic magnetic fields.

Contribution

It synthesizes recent developments and proposes a mechanism linking five-dimensional Chern-Simons theory to intergalactic magnetic fields.

Findings

Chern-Simons theory explains phenomena in knot theory and quantum Hall effects.

A proposed mechanism connects higher-dimensional Chern-Simons theory to cosmic magnetic fields.

The review emphasizes the interdisciplinary significance of Chern-Simons actions.

Abstract

Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the (integer and fractional) quantum Hall effect. A mechanism related to five-dimensional abelian Chern-Simons theory that may be at the origin of the observed intergalactic magnetic fields in the universe is described.