Global Quantization of Vacuum Angle and Magnetic Monopoles as a New Solution to the Strong CP Problem

TL;DR

This paper proposes a novel solution to the strong CP problem by linking magnetic monopoles to the quantization of the vacuum angle θ, suggesting that the existence of monopoles naturally explains the smallness or absence of CP violation.

Contribution

It introduces a new approach where magnetic monopoles enforce θ quantization, providing a non-perturbative solution to the strong CP problem with implications for the universe's openness.

Findings

Vacuum angle θ is quantized as 0 or multiples of 2π/n due to monopole structure.

Existence of magnetic monopoles with charge ±1 naturally solves the strong CP problem.

The solution remains valid even for very large total magnetic charges.

Abstract

The non-perturbative solution to the strong CP problem with magnetic monopoles as originally proposed by the author is described. It is shown that the gauge orbit space with gauge potentials and gauge tranformations restricted on the space boundary and the globally well-defined gauge subgroup in gauge theories with a $\theta$ term has a monopole structure if there is a magnetic monopole in the ordinary space. The Dirac's quantization condition then ensures that the vacuum angle $\theta$ in the gauge theories must be quantized to have a well-defined physical wave functional. The quantization rule for $\theta$ is derived as $\theta=0, 2\pi/n~(n\neq 0)$ with n being the topological charge of the magnetic monopole. Therefore, the strong CP problem is automatically solved with the existence of a magnetic monopole of charge $\pm 1$ with $\theta=\pm 2\pi$. This is also true when the total magnetic charge of monopoles are very large ($|n|\geq 10^92\pi$). The fact that the strong CP violation can be only so small or vanishing may be a signal for the existence of magnetic monopoles and the universe is open.