Dyons with phase ${\delta }_{\theta }=n\theta$

Abstract

In a recent paper (Heras in Eur. Phys. J. Plus 138: 329, 2023), we have demonstrated that when a dyon encircles an infinitely long solenoid enclosing electric and magnetic fluxes, its wave function accumulates a quantum phase invariant under electromagnetic duality transformations. In this paper, we show that this phase, in conjunction with the Witten effect, gives rise to a topological phase proportional to the vacuum angle $\theta$ and thereby connected with CP violation. We show that this phase becomes quantised in a vacuum state ${\delta }_{\theta }=n\theta$ and that the most general vacuum state associated with this quantisation identifies with an Abelian form of the $\theta$-vacua. We discuss two hypothetical interference effects in the vacuum where the angle $\theta$ could manifest.

v2. A minor typo was corrected in the abstract. Published in The European Physical Journal Plus. See the related preceding paper, arXiv:1910.01117

References in corpus (4)

• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Josephson currents induced by the Witten effect
• Topology, nonlocality and duality in classical electrodynamics
• The Aharonov-Bohm effect in a closed flux line