Higher order topological invariants from the Chern-Simons action

TL;DR

This paper explores how specific choices of Wilson lines in Chern-Simons field theory can produce higher order topological invariants beyond the standard linking numbers, enriching the understanding of topological quantum field theories.

Contribution

It introduces a method to obtain higher order topological invariants from the Chern-Simons action by selecting particular Wilson lines, extending the known link invariants.

Findings

Higher order topological linkings can be derived from the Chern-Simons action.

Standard Gaussian linkings are a special case of the more general invariants.

The approach provides new tools for studying topological properties in quantum field theories.

Abstract

It is well known that for a field theory with the Chern-Simons action, expectation values of Wilson line operators are topological invariants. The standard result is expressed in terms of the Gaussian linkings of closed curves defining the operators. We show how judicious choice of Wilson lines leads to higher order topological linkings.