A Topological Field Theory With a Finite Number of Connected Feynman Diagrams

TL;DR

This paper introduces a novel topological field theory with only two connected Feynman diagrams, combining features of abelian and non-abelian theories, and explores its associated topological invariants.

Contribution

It constructs a new topological field theory with a simplified perturbative expansion and identifies a new topological invariant from Wilson loop amplitudes.

Findings

Perturbative expansion contains only two connected diagrams.

Wilson loop amplitudes generate a new topological invariant.

The theory combines features of abelian and non-abelian Chern-Simons theories.

Abstract

A new topological field theory is constructed, which is characterized by cubic interactions similar to those of non-abelian Chern-Simons field theories, but still retains the simplicity of the abelian case. The perturbative expansion of this theory contains in fact only two connected Feynman diagrams, the propagator and a three vertex. Apart from the Gauss linking number, the Wilson loop amplitudes generate a further topological invariant, whose physical and mathematical meaning is investigated.