Does the Gursey-Tze Solution Represent a Monopole Condensate?

TL;DR

This paper analyzes the quaternionic Gursey-Tze solution, recasting it into a coordinate form, and suggests it may represent a monopole condensate in pure Yang-Mills theory, providing a potential concrete realization.

Contribution

It demonstrates that the Gursey-Tze solution can be interpreted as a monopole condensate in Yang-Mills theory through coordinate reformulation and summation techniques.

Findings

The solution is a self-dual Yang-Mills field with quasi-periodic structure.

After summation, it suggests a monopole per lattice cell configuration.

Potential realization of monopole condensate in pure Yang-Mills theory.

Abstract

We recast the quaternionic Gursey-Tze solution, which is a fourfold quasi-periodic self-dual Yang-Mills field with a unit instanton number per Euclidean spacetime cell, into an ordinary coordinate formulation. After performing the sum in the Euclidean time direction, we use an observation by Rossi which suggests the solution represents an arrangement with a BPS monopole per space lattice cell. This may provide a concrete realization of a monopole condensate in pure Yang-Mills theory.