Hurwitz numbers from Feynman diagrams

TL;DR

This paper establishes a novel connection between Hurwitz numbers and Feynman diagrams, showing how to compute the former using diagram enumeration techniques.

Contribution

It introduces a new method to derive Hurwitz numbers through counting specific Feynman diagrams and accounting for their automorphisms.

Findings

Hurwitz numbers can be expressed as Feynman diagram counts.

Automorphism groups of diagrams play a key role in the enumeration.

The approach provides a combinatorial interpretation of Hurwitz numbers.

Abstract

We obtain Hurwitz numbers as the number of Feynman diagrams of a certain type divided by the order of the automorphism group of the diagram.