Abstract
A Nielsen-Olesen vortex usually sits in an environment that expels the flux that 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 the vortex also permeates the `bulk' far from the vortex. The idea is to mix the vortex's internal gauge flux with an external flux using off-diagonal kinetic mixing. Such `dark' vortices could play a phenomenological role in models with both cosmic strings and a dark gauge sector. When coupled to gravity they also provide explicit ultra-violet completions for codimension-two brane-localized flux, which arises in extra-dimensional models when the same flux that stabilizes extra-dimensional size is also localized on space-filling branes situated around the extra dimensions. We derive simple formulae for observables such as defect angle, tension, localized flux and on-vortex curvature when coupled to gravity, and show how all of these are insensitive to much of the microscopic details of the solutions, and are instead largely dictated by low-energy quantities. We derive the required effective description in terms of a world-sheet brane action, and derive the matching conditions for its couplings. We consider the case where the dimensions transverse to the bulk compactify, and determine how the on- and off-vortex curvatures and other bulk features depend on the vortex properties. We find that the brane-localized flux does not gravitate, but just renormalizes the tension in a magnetic-field independent way. The existence of an explicit UV completion puts the effective description of these models on a more precise footing, verifying that brane-localized flux can be consistent with sensible UV physics and resolving some apparent paradoxes that can arise with a naive (but commonly used) delta-function treatment of the brane's localization within the bulk.
Highlights
The existence of an explicit UV completion puts the effective description of these models on a more precise footing, verifying that brane-localized flux can be consistent with sensible UV physics and resolving some apparent paradoxes that can arise with a naive delta-function treatment of the brane’s localization within the bulk
Appendix A proves this as a general consequence of stress-energy conservation within the vortex, with the vortex dynamically adjusting to ensure it is true. (Alternatively, the vanishing of X v on flat space can be derived as a consequence of making the vortex action stationary with respect to rescalings of the size of the vortex.) More generally, for curved geometries we find numerically that in the generic situation when rv ∼ rB all terms in (3.20) are similar in size and not small, but this is no longer true once a hierarchy in scales exists between the size of the vortex and that of the transverse dimensions
In this paper we investigated the gravitational properties of branes that carry localized flux of a bulk field, or BLF branes
Summary
Why study the gravitational response of Dark Vortices? Vortices are among the simplest stable solitons and arise in many theories with spontaneously broken U(1) gauge symmetries [7]. In theories with more than one U(1) factor more complicated patterns can exist, for which magnetic fields outside the vortex can acquire a localized intra-vortex component Such vortices naturally arise in ‘Dark Photon’ models [10, 11], for which the ordinary photon mixes kinetically [12] with a second, spontaneously broken, U(1) gauge field (as have been widely studied as Dark Matter candidates [13,14,15]). Cosmic strings of this type could carry localized ordinary magnetic flux, even though the U(1)EM gauge group remains unbroken [1,2,3,4,5,6]. We make this application in a companion paper [45, 46]
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