Related papers: Critical points and supersymmetric vacua
Let f be a smooth Morse function on an infinite dimensional separable Hilbert manifold, all of whose critical points have infinite Morse index and co-index. For any critical point x choose an integer a(x) arbitrarily. Then there exists a…
One of the goals of the landscape program in string theory is to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory.…
We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk…
For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$, we prove that the local eigenvalue statistics of $A+X$ close to the critical edge points of its spectrum are universal. This concludes the proof…
We investigate in detail solutions of supergravity that involve warped products of flat geometries of the type M(p+1) x R x T(D-p-2) depending on a single coordinate. In the absence of fluxes, the solutions include flat space and…
The zeros of complex Gaussian random polynomials, with coefficients such that the density in the underlying complex space is uniform, are known to have the same statistical properties as the zeros of the coherent state representation of…
The discovery that the number of physically consistent string vacua is on the order of 10^500 has prompted several statistical studies of string phenomenology. Contained here is one such study that focuses on the Weakly Coupled Free…
In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with $\mathscr{C}^3$ Hermitian metrics over a compact K\"{a}hler manifold.…
We continue the study of the distribution of nonsupersymmetric flux vacua in IIb string theory compactified on Calabi-Yau manifolds, as in hep-th/0404116. We show that the basic structure of this problem is that of finding eigenvectors of…
We study the role of multi-particle spatial correlations in the appearance of a liquid-vapour critical point. Our analysis is based on the exact infinite hierarchy of equations relating spatial integrals of $(k+1)$-particle correlations to…
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a…
We give an asymptotic probabilistic real Riemann-Hurwitz formula computing the expected real ramification index of a random covering over the Riemann sphere. More generally, we study the asymptotic expected number and distribution of…
Under an appropriate symmetric bulk bipartition in a one-dimensional symmetry protected topological phase with the Affleck-Kennedy-Lieb-Tasaki matrix product state wave function for the odd integer spin chains, a bulk critical entanglement…
New recent results in supersymmetric gauge theories based on holomorphy and symmetry considerations are extended to the case where the gauge coupling constant is given by the real part of a chiral superfield. We assume here that its…
There is growing evidence that the small weak scale may be related to self-organized criticality. In this regard, we note that if the strange quark were lighter, the QCD phase transition could have been first order, possibly exhibiting…
We study two-dimensional N=(4,4) supersymmetric gauge theories which do not have classical Higgs branches, but are believed to have isolated quantum Higgs vacua. We provide arguments for the existence of such vacua based on brane dynamics…
It is shown that different ways of interacting strings formed in high energy nucleus-nucleus collisions cause a different strength of the chaoticity parameter lambda of Bose-Einstein correlations. In particular, in the case of percolation…
In string theory with flux compactifications, anthropic selection for structure formation from a discretuum of vacuum energy values provides at present our only understanding of the tiny yet positive value of the cosmological constant. We…
Any multivariate distribution can be uniquely decomposed into marginal (1-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an…
The quest for the Standard Model among the huge number of string vacua is usually based on a set of phenomenological criteria related to the massless spectrum of string models. In this work we study criteria associated with interactions in…