Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects

TL;DR

This paper explores two-dimensional Yang-Mills gauge theory, focusing on its topological, geometric, and probabilistic features on the plane and compact surfaces.

Contribution

It provides a comprehensive analysis of 2D Yang-Mills theory emphasizing topological, geometric, and probabilistic perspectives, which enhances understanding of its mathematical structure.

Findings

Characterization of gauge theory on various surfaces

Insights into the probabilistic structure of gauge fields

Connections between topology and gauge theory

Abstract

We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.