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Vortices in spin-$0$ superfluids generically carry magnetic fields insidetheir cores, so that even neutral superfluid vortices may be thought of asmagnetic flux tubes. We give a systematic analysis of this `vortex magneticeffect' using effective field theory, clarifying earlier literature on thesubject. Our analysis shows that in superfluid Helium-$4$ the vortex magneticeffect may be large enough to be experimentally detectable.

Vortices in spin-0 superfluids carry magnetic flux