EFT for vortices with dilaton-dependent localized flux

Abstract

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 [10] 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 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. In passing we show why a common procedure for doing so using a δ-function can lead to incorrect results. Our procedures generalize straightforwardly to general co-dimension objects.

The gravity of dark vortices: effective field theory for branes and strings carrying localized flux

“…Although extra-dimensional branes are not in themselves expected to be sufficient to provide a solution (for instance, one must also deal with the higher-dimensional cosmological constant), the techniques developed here can also be applied to their supersymmetric alternatives [42][43][44], for which higher-derivative cosmological constants are forbidden by supersymmetry and whose ultimate prospects remain open at this point. We make this application in a companion paper [45,46].…”

“…Lastly, we plan [45,46] to also apply these techniques to a supersymmetric brane-world models that aim to tackle the cosmological constant problem [42][43][44]. The back-reaction of branes is a crucial ingredient of such models, and understanding the system in greater detail with an explicit UV completion will put these models on firmer ground and hopefully shed light on new angles from which to attack the CC problem.…”

Self-tuning at large (distances): 4D description of runaway dilaton capture

“…This is important because the system often responds to perturbations by moving flux onto and off of the branes, since it is energetically inexpensive to change the value of φ. We use the effective theory that captures the low-energy dynamics of this flux in the higher-dimensional theorydeveloped in companion papers [1,2] -to work out the effective 4D description provided here, identifying in particular the precise form of the scalar potential that governs the energetics of vacuum determination. We find the following main results.…”

“…More recently [2] -see also [37,38] -it was found that the absence of dilaton couplings is not as straightforward as demanding dilaton-independence of the brane tension and BLF coefficient, A(φ), of (1.1), due…”

“…Our interest is in situations where the back-reaction of the branes breaks a degeneracy of the bulk system and lifts an otherwise flat direction. As in two earlier papers [1,2] we focus on systems for which the interactions are weak enough to ensure that the energetics lifting this flat direction are amenable to understanding in the effective 4D theory below the Kaluza-Klein (KK) scale. We compute this low-energy potential explicitly within the classical limit, to identify how it depends on the various parameters describing the underlying UV completion.…”