  In quantum electrodynamics, the zero-charge effect originates from the
logarithmic dependence of the coupling constant in the action of the
electromagnetic field on the ratio of the ultraviolet and infrared energy
cutoffs. An analogue of this effect in Weyl superfluid $^3$He-A is the
logarithmic divergence of the bending energy of the orbital anisotropy axis at
low temperatures, where temperature plays the role of the infrared cutoff and
the vector of the orbital anisotropy plays the role of the vector potential of
the synthetic electromagnetic field for Weyl fermions. We calculate numerically
the spatial distribution of the order parameter in rotating $^3$He-A as a
function of temperature. At temperatures close to the superfluid transition, we
observe formation of vortex skyrmions known as the double-quantum vortex and
the vortex sheet. These structures include alternating circular and hyperbolic
merons as a bound pair or a chain, respectively. As temperature lowers towards
absolute zero, we find a continuous transition in the vortex structures towards
a state where the vorticity is distributed in thin tubes around the circular
merons. For the vortex sheet, we present a phase diagram of the transition in
the temperature - angular velocity plane and calculations of the nuclear
magnetic resonance response.
