Abstract
We study how codimension-two objects like vortices back-react gravitationally with their environment in theories (such as 4D or higher-dimensional supergravity) where the bulk is described by a dilaton-Maxwell-Einstein system. We do so both in the full theory, for which the vortex is an explicit classical `fat brane' solution, and in the effective theory of `point branes' appropriate when the vortices are much smaller than the scales of interest for their back-reaction (such as the transverse Kaluza-Klein scale). We extend the standard Nambu-Goto description to include the physics of flux-localization wherein the ambient flux of the external Maxwell field becomes partially localized to the vortex, generalizing the results of a companion paper to include dilaton-dependence for the tension and localized flux. In the effective theory, such flux-localization is described by the next-to-leading effective interaction, and the boundary conditions to which it gives rise are known to play an important role in how (and whether) the vortex causes supersymmetry to break in the bulk. We track how both tension and localized flux determine the curvature of the space-filling dimensions. Our calculations provide the tools required for computing how scale-breaking vortex interactions can stabilize the extra-dimensional size by lifting the dilaton's flat direction. For small vortices we derive a simple relation between the near-vortex boundary conditions of bulk fields as a function of the tension and localized flux in the vortex action that provides the most efficient means for calculating how physical vortices mutually interact without requiring a complete construction of their internal structure. In passing we show why a common procedure for doing so using a $\delta$-function can lead to incorrect results. Our procedures generalize straightforwardly to general co-dimension objects.
Highlights
The relative size of their tension and the amount localized bulk flux they carry [11, 12]
In the effective theory, such flux-localization is described by the next-to-leading effective interaction, and the boundary conditions to which it gives rise are known to play an important role in how the vortex causes supersymmetry to break in the bulk
For small vortices we derive a simple relation between the nearvortex boundary conditions of bulk fields as a function of the tension and localized flux in the vortex action that provides the most efficient means for calculating how physical vortices mutually interact without requiring a complete construction of their internal structure
Summary
We start by outlining the action and field equations of the bulk, which we take to be an Einstein-Maxwell-scalar system. Our goal is to understand how bulk properties (such as curvatures) are related to the asymptotic behaviour of the fields near any localized sources. We return in later sections describing the local sources in terms of vortices, with the goal of understanding what features of the source control the near-source asymptotics. We imagine the bulk to span D = d + 2 spacetime dimensions with the d-dimensional sources localized in two transverse dimensions. Since this section on the bulk duplicates standard results [15, 21,22,23, 32,33,34], aficionados in a hurry should skip it and go directly to the section
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