Magnetic Monopoles and Topology of Yang-Mills Theory in Polyakov Gauge

TL;DR

This paper demonstrates that the Pontryagin index in Yang-Mills theory, when expressed in Polyakov gauge, can be fully characterized by magnetic monopoles, linking topological invariants to gauge fixing defects.

Contribution

It provides a novel formulation of the Pontryagin index solely in terms of magnetic monopoles within Polyakov gauge, clarifying their topological role.

Findings

Pontryagin index expressed via magnetic monopoles

Open lines and domain walls are topologically equivalent to monopoles

Smooth gauge fixing avoids non-genuine magnetic defects

Abstract

We express the Pontryagin index in Polyakov gauge completely in terms of magnetically charged gauge fixing defects, namely magnetic monopoles, lines, and domain walls. Open lines and domain walls are topologically equivalent to monopoles, which are the genuine defects. The emergence of non-genuine magnetically charged closed domain walls can be avoided by choosing the temporal gauge field smoothly. The Pontryagin index is then exclusively determined by the magnetic monopoles.