Magnetic monopoles as a new solution to strong CP problem

Abstract

A non-perturbative solution to strong CP problem is proposed. It is shown that the gauge orbit space with gauge potentials and well-defined gauge transformations topologically restricted on the space boundary in non-abelian gauge theories with a θ term has a 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 for θ is derived as θ = 0,2 π/ n ( n ≠ 0) with n being the topological charge we obtain for the magnetic monopole. Therefore, the strong CP problem is automatically solved non-perturbatively in the presence of magnetic monopoles, with charge ±1 so that θ = ±2 π, or with a very large (| n| ⩾ 10 9 × 2 π) total topological charge for the same generator, or with non-abelian monopoles of more than one non-zero n i corresponding to color SU(3) so that the relevant effective θ = 0. 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. If there exists an axion field a( x), the value of the physical axion field a phy( x) will not be quantized. However, the expectation value of the CP violating density ϵ μνγσ F μσ a F γσ a will be quantized. For the special values of the topological number n, it can be vanishing or very small even without using the Peccei-Quinn dynamical adjusting. In the usual gauge theories without magnetic monopoles, there may be at most a Z 2 monopole structure in the gauge orbit space in SP(2 N) gauge theories.