Magnetic Monopoles As a New Solution to Strong CP Problem

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A non-perturbative solution to strong CP problem is proposed. It is shown that the gauge orbit space with gauge potentials and gauge tranformations restricted on the space boundary in non-abelian gauge theories with a θ term has a magnetic monopole structure if there is a magnetic monopole in the ordinary space. The Dirac's quantization condition in the corresponding quantum theories ensures that the vacuum angle θ in the gauge theories must be quantized. The quantization rule is derived as θ=2π/n (n≠ 0) with n being the topological charge of the magnetic monopole. Therefore, we conclude that the strong CP problem is automatically solved non-perturbatively with the existence of a magnetic monopole of charge ± 1 with θ=± 2π. This is also true when the total magnetic charge of monopoles are very large (|n|≥ 10⁹2π) if it is consistent with the abundance of magnetic monopoles. This implies that the fact that the strong CP violation can be only so small or vanishing may be a signal for the existence of magnetic monopoles.