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Abstract:

We study a number of realizations of axions existing in a multi-`throat' generalization of the warped throat geometry of a Randall-Sundrum slice of $AdS_5$. As argued by previous authors, the problem of generating a suitable, phenomenologically allowed Peccei-Quinn scale is simply and elegantly solved by the warping. In compactifications with two or more throats it is possible to simultaneously solve the Standard Model hierarchy problem by the Randall-Sundrum mechanism while implementing interesting warped axion models. The constructions discussed are related to holographic duals of previously studied models of composite axions arising from strongly coupled four-dimensional dynamics.

Abstract:

We attempt to quantify the widely-held belief that large hierarchies induced by strongly-warped geometries are common in the string theory landscape. To this end, we focus on the arguably best-understood subset of vacua -- type IIB Calabi-Yau orientifolds with non-perturbative Kaehler stabilization and a SUSY-breaking uplift (the KKLT setup). Within this framework, vacua with a realistically small cosmological constant are expected to come from Calabi-Yaus with a large number of 3-cycles. For appropriate choices of flux numbers, many of these 3-cycles can, in general, shrink to produce near-conifold geometries. Thus, a simple statistical analysis in the spirit of Denef and Douglas allows us to estimate the expected number and length of Klebanov-Strassler throats in the given set of vacua. We find that throats capable of explaining the electroweak hierarchy are expected to be present in a large fraction of the landscape vacua while shorter throats are essentially unavoidable in a statistical sense.