Surface-Invariants in 2D Classical Yang-Mills Theory

TL;DR

This paper develops a method to derive area-preserving diffeomorphism invariants from 2D classical Yang-Mills theory, using a perturbative approach with charged particles, and provides a geometric interpretation of these invariants.

Contribution

It introduces a novel perturbative scheme to extract area-invariants from classical Yang-Mills theory coupled to charged particles, with a geometric understanding.

Findings

First two area-invariants obtained from the on-shell action

Geometric interpretation of the invariants provided

Perturbative scheme successfully applied to classical Yang-Mills

Abstract

We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to non dynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on shell action, which are area-invariants. A geometrical interpretation of these invariants is given.