Role of the equivalence principle in gauge and axial symmetries of Yukawa coupling, and the strong CP problem

Abstract

It is demonstrated the fundamental role of the equivalence principle in gravity for the Yukawa coupling between scalar and fermion fields. The Kibble-Zurek mechanism for formation of topological defects as vortexes and monopoles breaks down in system with a global gauge symmetry only. At the same time, the different vacuums can occur, which are separated be domain walls. The equivalence principle makes the strong violation of CP invariance impossible. Thus the axion hypothesis becomes redundant.

Figures (5)

• Figure 1: the scalar field $\varphi$ from position 0 at the top of the hill rolls down into the valley, for example, to positions 1 or 2 or 3 having the equal energies. To each position we can assign an angular coordinate $\theta=0$.
• Figure 2: configuration of scalar field $\varphi$ (arrows indicate the phase): (a,b,c) - in each point of space the scalar field has the same equilibrium phases $\varphi=|\varphi(x)|e^{\theta_{0}}$, and energies of the (a,b,c) are equal, then the phase value can be assigned to $\theta_{0}=0$, no matter in which phase $\theta$ the field has rolled. (d) - vortex, where there is a line with value of the scalar field $\varphi=0$ (in center of "hedgehog"), and magnetic field $\mathbf{B}$ (blue color) is directed along this axis, the concentric lines of vector-potential $\mathbf{A}$ are shown by green color.
• Figure 3: transformation of vertexes of Yukawa coupling due to the absorption of phase oscillations $\theta(x)$ by the gauge field $A_{\mu}$ (Higgs effect): Dirac fields $\psi_{L,R}$ interact with module of the scalar field $|\varphi|$.
• Figure 4: distribution of phase of the scalar field $\varphi=|\varphi|e^{i\theta}$ throughout the entire space conditionally consisting of cells of the order cosmological horizon $\sim \frac{c}{H}$: (a) - evolution to either uniform distribution or to a topological defect as the horizon increases (the Hubble parameter $H$ decreases), (b) - application of the equivalence principle for Yukawa coupling results in the phase being assigned as $\theta=0$ in all cells, i.e Kibble–Zurek mechanism breaks down.
• Figure 5: the mechanical analogy of the transmission of rotation from isospinor (scalar) field $\Psi$ to Dirac field $\psi$ via the gauge fields $\vec{A}_{\mu},B_{\mu}$ and vice versa. Rotation from the engine is transmitted to the wheels via the clutch - gauge fields. And vice versa: you can rotate the wheels and this rotation will be transmitted to the engine shaft via the clutch. However, in the case of rotation by the global gauge transformations, the clutch is not cuddled and, as a consequence, the backlash in rotation occurs.