Metastable Vacua in Warped Throats at Non-Isolated Singularities

We study the existence of metastable vacua in cascades based on fractional brane configurations at non-isolated singularities preserving N = 1 supersymmetry. We find that in a large class of models the extra moduli typically generated along such cascades may be stabilized by utilizing special monopole points found recently. We illustrate this in detail for cascades based on the SPP singularity. The supergravity interpretation of these constructions in terms of warped throats with supersymmetry breaking localized near their tips as well as applications to string compactification is discussed. Our constructions are designed to realize a large class of warped throats with supersymmetry breaking localized inside of a highly curved tip region.Comment: 18 pages, added clarifications, published version; 1 figur

On some intermediate mean values

We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class $\Lambda_{f,g}(a, b)$ of mean values where $f, g$ are continuously differentiable convex functions satisfying the relation $f"(t)=t g"(t), t\in \Bbb R^+$. Then we asked for a characterization of $f, g$ such that the inequalities $H(a, b)\le \Lambda_{f, g}(a, b)\le A(a, b)$ or $L(a, b)\le \Lambda_{f, g}(a, b)\le I(a, b)$ hold for each positive $a, b$, where $H, A, L, I$ are the harmonic, arithmetic, logarithmic and identric means, respectively. For a subclass of $\Lambda$ with $g"(t)=t^s, s\in \Bbb R$, this problem is thoroughly solved

On a Hierarchy of Means

For a class of partially ordered means we introduce a notion of the (nontrivial) cancelling mean. A simple method is given which helps to determine cancelling means for well known classes of Holder and Stolarsky means