Invariants from classical field theory

TL;DR

This paper presents a method to generate invariants from classical field theories, applying it to various models to recover known topological invariants and discover new ones.

Contribution

It introduces a novel approach to derive invariants from perturbative classical field theories, connecting physics and topology.

Findings

Linking number for embedded submanifolds in compact varieties

Gauss' and Milnor's invariants for links in S^3

Invariants under area-preserving diffeomorphisms for immersed planar curves

Abstract

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S^3, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.