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The Ubiquitous Throat

A. Hebecker, J. March-Russell

TL;DR

This work argues that strongly warped Klebanov-Strassler throats are a generic feature of the KKLT-type IIB flux landscape with many 3-cycles. By combining flux vacuum counting near conifold points with multi-modulus stabilization and uplift, the authors derive simple, testable predictions for the distribution and length of throats: the number of throats with hierarchy above a threshold follows a binomial law with mean $\bar{n} = \frac{K}{3c\log h_*}$ and the longest throat scales as $\log h_1 \sim \frac{K}{3c}$. Depending on $K$ and $c$, short throats ($\sim 10^3$ hierarchy) are common, while electroweak- and even meV-scale throats can be frequent or plausible, implying potentially observable or cosmologically relevant hidden sectors. The analysis relies on the density of flux vacua near conifold points and assumes a multi-modulus stabilization framework where stability after uplift is generically maintained. Overall, throats emerge as a firm and influential prediction of the type IIB landscape, with important implications for phenomenology and cosmology, while acknowledging sensitive dependence on unknown high-dimensional data such as $K$ and $L_*$.

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.

The Ubiquitous Throat

TL;DR

This work argues that strongly warped Klebanov-Strassler throats are a generic feature of the KKLT-type IIB flux landscape with many 3-cycles. By combining flux vacuum counting near conifold points with multi-modulus stabilization and uplift, the authors derive simple, testable predictions for the distribution and length of throats: the number of throats with hierarchy above a threshold follows a binomial law with mean and the longest throat scales as . Depending on and , short throats ( hierarchy) are common, while electroweak- and even meV-scale throats can be frequent or plausible, implying potentially observable or cosmologically relevant hidden sectors. The analysis relies on the density of flux vacua near conifold points and assumes a multi-modulus stabilization framework where stability after uplift is generically maintained. Overall, throats emerge as a firm and influential prediction of the type IIB landscape, with important implications for phenomenology and cosmology, while acknowledging sensitive dependence on unknown high-dimensional data such as and .

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.

Paper Structure

This paper contains 6 sections, 30 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The relevant set of vacua
  3. Stability issues
  4. The distribution of throats
  5. Possible phenomenological implications
  6. Conclusions

Figures (1)

  • Figure 1: Probability that at least one throat has hierarchy $h>h_*$ as a function of $\log h_*$. Reading from bottom to top the curves correspond to the choices $K=60$ and 200 (both taking $c=1$).