Related papers: Spectral geometry for strings and branes
In this thesis I present a new type of brane - H-brane - where the role of time in String Theory is considered as a primary concept in the search for still unknown black hole physics. Using the basic tools of boundary conformal field…
I review recent progress on the connection between string theory and quantum chromodynamics in the context of the gauge/gravity duality. Emphasis is placed on conciseness and conceptual aspects rather than on technical details. Topics…
We review the construction of the $D$-branes at finite temperature as boundary states in the Fock space of thermal perturbative closed string. This is a talk presented by I. V. V. at Common Trends in Cosmology and Particle Physics June…
Decoupling limits of physical interest occur in regions of space--time where the string coupling diverges. This is illustrated in the celebrated example of five-branes. There are several ways to overcome this strong-coupling problem. We…
The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic differential second order operator is generalized to manifolds with boundary. The first boundary coefficients of the asymptotic expansion which are…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems,…
In this thesis we discuss some topics about topology and superstring backgrounds with D-branes. We start with a mathematical review about generalized homology and cohomology theories and the Atiyah-Hirzebruch spectral sequence, in order to…
Let $G$ be a noncompact semisimple Lie group equipped with a certain invariant Riemannian metric. Then, we can consider a heat kernel function on $G$ associated to the Riemannian metric. We give an explicit formula for the heat kernel when…
This paper is an exposition of several questions linking heat kernel measures on infinite dimensional Lie groups, limits associated with critical Sobolev exponents, and Feynmann-Kac measures for sigma models.
We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent…
The aim of our paper is twofold. First, we present new mathematical developments on the analysis of de Gennes' hypothesis on the short-time asymptotics of the heat content for bounded domains with smooth boundary and with fractal boundary.…
This thesis concerns the study of high-temperature string theory on curved backgrounds, generalizing the notions of Hagedorn temperature and thermal scalar to general backgrounds. Chapter 2 contains a review on string thermodynamics in flat…
This article shows that under locally uniformly integral bounds of the negative part of Ricci curvature the heat kernel admits a Gaussian upper bound for small times. This provides general assumptions on the geometry of a manifold such that…
We argue about the importance of embedding the successful mechanism of Inflation in the context of a fundamental theory. We review some of the attempts in this direction made in the framework of String Theory. In particular we report on…
In this thesis we discuss some nonperturbative and noncommutative aspects of string theory. We present low-energy background field solutions corresponding to various D-branes (and their bound states) and intersecting branes in flat and…
Let $(M,g)$ be a surface with Riemannian metric and curved conic singularities. More precisely, a neighbourhood of a singularity is isometric to $(0,1)\times S^1$ with metric $g_{\text{conic}}=dr^2+f(r)^2d\theta^2, r\in(0,1)$. We study the…
We review some recent results on the extension of the gauge/gravity correspondence to include matter in the fundamental representation by adding D-branes to the supergravity backgrounds. Working in the quenched approximation, in which the…
We prove pointwise and $L^p$ gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hodge semigroup in that setting and prove estimates for its…
We have obtained an explicit expression for the spectral zeta functions and for the heat kernel of strings, drums and quantum billiards working to third order in perturbation theory, using a generalization of the binomial theorem to…