YANG-MILLS THEORY WITH THE PONTRYAGIN TERM ON MANIFOLDS WITH A BOUNDARY

TL;DR

This paper investigates the structure and quantization of 3+1 dimensional Yang-Mills theory with a Pontryagin term on manifolds with boundaries, emphasizing geometric and topological aspects.

Contribution

It introduces a geometric framework for the symplectic structure and topological quantization line bundles in Yang-Mills theory with boundary conditions.

Findings

Symplectic structure derived from the universal bundle geometry.

Quantization line bundle topology linked to torsion in gauge orbit cohomology.

Insights into boundary effects in Yang-Mills theory.

Abstract

The 3+1 dimensional Yang-Mills theory with the Pontryagin term included is studied on manifolds with a boundary. Based on the geometry of the universal bundle for Yang-Mills theory, the symplectic structure of this model is exhibited. The topological type of the quantization line bundles is shown to be determined by the torsion elements in the cohomology of the gauge orbit space.