Local random potentials of high differentiability to model the Landscape
| Autor: | Battefeld, Thorsten, Modi, Chirag |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | JCAP 03 (2015) 010 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1475-7516/2015/03/010 |
| Popis: | We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., smooth first and second derivatives for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (D ~ 100). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications. Comment: V2: added discussion section to match published version (conclusions unchanged); 25 pages, 5 figures |
| Databáze: | arXiv |
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