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

Abstract

Abstract:We complete here a three-part study (see also arXiv:1506.08095 and arXiv:1508.00856) of how codimension-two objects back-react gravitationally with their environment, with particular interest in situations where the transverse 'bulk' is stabilized by the interplay between gravity and flux-quantization in a dilaton-Maxwell-Einstein system such as commonly appears in higher-dimensional supergravity and is used in the Supersymmetric Large Extra Dimensions (SLED) program. Such systems enjoy a classical flat direction that can be lifted by interactions with the branes, giving a mass to the would-be modulus that is smaller than the KK scale. We construct the effective low-energy 4D description appropriate below the KK scale once the transverse extra dimensions are integrated out, and show that it reproduces the predictions of the full UV theory for how the vacuum energy and modulus mass depend on the properties of the branes and stabilizing fluxes. In particular we show how this 4D theory learns the news of flux quantization through the existence of a space-filling four-form potential that descends from the higherdimensional Maxwell field. We find a scalar potential consistent with general constraints, like the runaway dictated by Weinberg's theorem. We show how scale-breaking brane interactions can give this potential minima for which the extra-dimensional size, , is exponentially large relative to underlying physics scales, r B , with 2 = r 2 B e −ϕ where −ϕ 1 can be arranged with a small hierarchy between fundamental parameters. We identify circumstances where the potential at the minimum can (but need not) be parametrically suppressed relative to the tensions of the branes, provide a preliminary discussion of the

EFT for vortices with dilaton-dependent localized flux

“…Integration over the transverse space can be regarded as projecting the field equations onto the zero mode in these directions, and so (3.83) can be interpreted as the equation that determines the value of the dilaton zero-mode. (This conclusion is also shown more explicitly from the point of view of the effective d-dimensional theory in a forthcoming analysis [69].) In the absence of the sources this zero mode is an exact flat direction of the classical equations associated with the scale invariance of the bulk field equations (for instance X B = 0 for the source-free Salam-Sezgin solution [70]) and the vortex contribution to (3.83) expresses how this flat direction becomes fixed when the sources are not scale-invariant.…”

“…We do so by adding new scalar and gauge fields that admit such vortex solutions, with a view to understanding in more detail how near-source behaviour is controlled by the source properties. Because our focus here is mostly on classical issues we do not explicitly embed the new sector into a supersymmetric framework, but we return to this issue when considering quantum corrections in subsequent analysis [69].…”

“…What the above expressions leave open is what this precise form is, since this requires a more detailed evaluation of the φ-dependence of all quantities that has been done here, including all of the φ-dependence implicit within X tot , and not just the near-source part X loc v estimated here. Although this takes us beyond the scope of this (already long) paper, we do describe such a more detailed calculation in [69], including a description of the 4D perspective obtained by integrating out the extra dimensions entirely.…”

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.…”