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 θ and thereby connected with CP violation. We show that this phase becomes quantised in a vacuum state δ_θ=nθ and that the most general vacuum state associated with this quantisation identifies with an Abelian form of the θ-vacua. We discuss two hypothetical interference effects in the vacuum where the angle θ could manifest.