Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories

TL;DR

This paper reviews recent advances in 2D Yang-Mills theory and the construction of topological field theories, highlighting the role of equivariant cohomology in their formulation and geometric interpretation.

Contribution

It provides an expository overview connecting 2D Yang-Mills, topological field theories, and equivariant cohomology from a geometric perspective.

Findings

Unifies 2D Yang-Mills and topological field theories through equivariant cohomology.

Clarifies the geometric interpretation of topological field theory path integrals.

Highlights the role of BRST symmetry in topological models.

Abstract

These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory, and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.