Towards a Complete Mass Spectrum of Type-IIB Flux Vacua at Large Complex Structure

The large number of moduli fields arising in a generic string theory compactification makes a complete computation of the low energy effective theory infeasible. A common strategy to solve this problem is to consider Calabi-Yau manifolds with discrete symmetries, which effectively reduce the number of moduli and make the computation of the truncated Effective Field Theory possible. In this approach, however, the couplings (e.g., the masses) of the truncated fields are left undetermined. In the present paper we discuss the tree-level mass spectrum of type-IIB flux compactifications at Large Complex Structure, focusing on models with a reduced one-dimensional complex structure sector. We compute the tree-level spectrum for the dilaton and complex structure moduli, including the truncated fields, which can be expressed entirely in terms of the known couplings of the reduced theory. We show that the masses of this set of fields are naturally heavy at vacua consistent with the KKLT construction, and we discuss other phenomenologically interesting scenarios where the spectrum involves fields much lighter than the gravitino. We also derive the probability distribution for the masses on the ensemble of flux vacua, and show that it exhibits universal features independent of the details of the compactification. We check our results on a large sample of flux vacua constructed in an orientifold of the Calabi-Yau WP[1,1,1,1,4]4. Finally, we also discuss the conditions under which the spectrum derived here could arise in more general compactifications

Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

Characterisation of vacua of the String Theory Landscape

Tesis en euskera 247 p.-- Tesis en inglés 247 p.[EU]Grabitate kuantikoaren teoria bateratzailea da Soka-Teoria. Aitzitik, teoriaren tinkotasuna bermatzeko 10 espazio-denborako dimentsiotan deskribatu behar dugu. Jakina, Soka-Teoria fenomenologikoki onargarria izan dadin, energia baxuko eremu-teoria eraginkorra 4 dimentsiotan deskribatu beharko dugu. Horretarako, espazio-denboraren gehiegizko dimentsio horiek nolabait trinkotu behar ditugu; adibidez, IIB motako Soka-Teoriaren gehiegizko 6 dimentsioen geometria Calabi-Yau espazioen bidez deskribatu ohi dira. Trinkoketa horien inguruko zenbait aspektu fenomenologiko aztertzea da tesi honen helburu nagusia. Barne-geometriaren oinarrizko ezaugarriak erabiliz, zuzenean froga daiteke trinkoketa horiek hainbat eratara deformatu daitezkeela energia-kosturik gabe. Horrenbestez, barnegeometria deskribatzen dituzten ehunka parametroak (moduluak) masarik gabeko eremu bezala joko dira lau dimentsioko ikuspuntu behagarriarengandik, eta hori bateraezina da gaur egungo behaketekin. Hori dela eta, nahitaezkoa zaigu modulu horiei masa ematea eta nolabait egonkortzea. Hartara, 1. kapituluan deskribatutakoaren arabera, teorian bertan ageri diren fluxuak erabili daitezke moduluen potentzial eskalar bat osatzeko. Ehunka dimentsioko potentzial eskalar horri Paisaia deritzo, horren egitura konplexua dela eta. Paisaiaren minimoek Soka-Teoriaren barne-geometriaren egoera egonkorrak adierazten dituzte; hortaz, horien inguruko ezagutza tinkoa izatea ezinbestekoa zaigu Soka-Teoriaren eredu fenomenologikoki zuzenak eraikitzeko.[ES]La Teoría de Cuerdas es uno de los candidatos principales a unificar todas las interacciones de lanaturaleza bajo un único marco. Sin embargo, una de sus principales características es que requiere lacompactificación de varias dimensiones extra para poder ser fenomenológicamente consistente. En eseproceso, se genera un potencial llamado "Paisaje", cuyos mínimos o vacíos representan configuracionesestables de la geometría compacta del espacio. El objetivo principal de esta tesis es estudiar esos vacíosteniendo en cuenta múltiples consideraciones fenomenológicas, particularmente desde una perspectivacosmológica. En la primera parte de la tesis, hemos explorado las características de estos vacíos desde unpunto de vista completamente analítico usando los ingredientes fundamentales de la teoría. En la segundaparte, analizamos los fenómenos cosmológicos que pueden darse en Paisajes formados por funcionesaleatorias que imitan la complejidad de este potencial, así como procesos de efecto túnel entre mínimosque requieren flujos y membranas. De esta manera, hemos podido hacer un análisis de este interesantepotencial desde diversos puntos de vista frecuentemente investigados en la literatura actual