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A Nielsen-Olesen vortex usually sits in an environment that expels the fluxthat is confined to the vortex, so flux is not present both inside and outside.We construct vortices for which this is not true, where the flux carried by thevortex also permeates the `bulk' far from the vortex. The idea is to mix thevortex's internal gauge flux with an external flux using off-diagonal kineticmixing. Such `dark' vortices could play a phenomenological role in models withboth cosmic strings and a dark gauge sector. When coupled to gravity they alsoprovide explicit ultra-violet completions for codimension-two brane-localizedflux, which arises in extra-dimensional models when the same flux thatstabilizes extra-dimensional size is also localized on space-filling branessituated around the extra dimensions. We derive simple formulae for observablessuch as defect angle, tension, localized flux and on-vortex curvature whencoupled to gravity, and show how all of these are insensitive to much of themicroscopic details of the solutions, and are instead largely dictated bylow-energy quantities. We derive the required effective description in terms ofa world-sheet brane action, and derive the matching conditions for itscouplings. We consider the case where the dimensions transverse to the bulkcompactify, and determine how the on- and off-vortex curvatures and other bulkfeatures depend on the vortex properties. We find that the brane-localized fluxdoes not gravitate, but just renormalizes the tension in a magnetic-fieldindependent way. The existence of an explicit UV completion puts the effectivedescription of these models on a more precise footing, verifying thatbrane-localized flux can be consistent with sensible UV physics and resolvingsome apparent paradoxes that can arise with a naive (but commonly used)delta-function treatment of the brane's localization within the bulk.

The Gravity of Dark Vortices: Effective Field Theory for Branes and Strings Carrying Localized Flux