The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces

TL;DR

This paper proves the Makeenko-Migdal equation for 2D Euclidean Yang-Mills theory on any compact surface, extending previous proofs from the plane to more general surfaces, including those with boundaries.

Contribution

It generalizes the proof of the Makeenko-Migdal equation from the plane to arbitrary compact surfaces, broadening its applicability in mathematical physics.

Findings

Proved the Makeenko-Migdal equation on compact surfaces.

Extended previous proofs from the plane case to compact surfaces.

Applicable to surfaces with boundary.

Abstract

We prove the Makeenko-Migdal equation for two-dimensional Euclidean Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In particular, we show that two of the proofs given by the first, third, and fourth authors for the plane case extend essentially without change to compact surfaces.