Large-N Yang-Mills Theory as Classical Mechanics

TL;DR

This paper reformulates large-N two-dimensional Yang-Mills theory with adjoint matter as classical mechanics by deriving a Poisson algebra for color-invariant observables, emphasizing topological graphical insights.

Contribution

It provides a pedagogical explanation of the topological graphical methods used to derive the Poisson algebra in large-N Yang-Mills theory.

Findings

Derived a Poisson algebra for observables involving adjoint matter

Showed quantum orderings lead to essentially the same algebra

Provided a pedagogical account of the topological graphical observations

Abstract

To formulate two-dimensional Yang-Mills theory with adjoint matter fields in the large-N limit as classical mechanics, we derive a Poisson algebra for the color-invariant observables involving adjoint matter fields. We showed rigorously in J. Math. Phys. 40, 1870 (1999) that different quantum orderings of the observables produce essentially the same Poisson algebra. Here we explain, in a less precise but more pedagogical manner, the crucial topological graphical observations underlying the formal proof.