John March-Russell

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.

Abstract:

We study the ΔI=1/2 rule for kaon decays and the BK parameter for K0-K̄0 mixing in a dual 5-dimensional holographic QCD model. We perform, in the chiral limit, computations of the relevant four-point current-current correlators, which depend upon self-interactions among the 5D bulk fields. Spontaneous chiral symmetry breaking (χSB) is realized through boundary conditions on the bulk fields. Numerical results are analyzed in comparison with QCD, chiral perturbation theory (χPT) and data, finding reasonable agreement with the experimental values of the g8 and g27 parameters describing the ΔI=1/2, 3/2 decay channels. © 2006 The American Physical Society.

Abstract:

Following Freivogel et al we consider inflation in a predictive (or 'friendly') region of the landscape of string vacua, as modeled by Arkani-Hamed, Dimopoulos and Kachru. In such a region the dimensionful coefficients of super-renormalizable operators unprotected by symmetries, such as the vacuum energy and scalar mass-squareds are freely scanned over, and the objects of study are anthropically or 'environmentally' conditioned probability distributions for observables. In this context we study the statistical predictions of (inverted) hybrid inflation models, where the properties of the inflaton are probabilistically distributed. We derive the resulting distributions of observables, including the deviation from flatness |1-Ω|, the spectral index of scalar cosmological perturbations ns (and its scale dependence dns/dlog k), and the ratio of tensor to scalar perturbations r. The environmental bound on the curvature implies a solution to the η-problem of inflation with the predicted distribution of (1-n s) indicating values close to current observations. We find a relatively low probability (< 3%) of 'just-so' inflation with measurable deviations from flatness. Intermediate scales of inflation are preferred in these models. © SISSA 2006.

Abstract:

Following Freivogel {\it et al} we consider inflation in a predictive (or `friendly') region of the landscape of string vacua, as modeled by Arkani-Hamed, Dimopoulos and Kachru. In such a region the dimensionful coefficients of super-renormalizable operators unprotected by symmetries, such as the vacuum energy and scalar mass-squareds are freely scanned over, and the objects of study are anthropically or `environmentally' conditioned probability distributions for observables. In this context we study the statistical predictions of (inverted) hybrid inflation models, where the properties of the inflaton are probabilistically distributed. We derive the resulting distributions of observables, including the deviation from flatness $|1-\Omega|$, the spectral index of scalar cosmological perturbations $n_s$ (and its scale dependence $dn_s/d\log k$), and the ratio of tensor to scalar perturbations $r$. The environmental bound on the curvature implies a solution to the $\eta$-problem of inflation with the predicted distribution of $(1-n_s)$ indicating values close to current observations. We find a relatively low probability ($<3%$) of `just-so' inflation with measurable deviations from flatness. Intermediate scales of inflation are preferred in these models.