publication . Preprint . Article . 2011

The wasteland of random supergravities

David Marsh; Liam McAllister; Timm Wrase;
Open Access English
  • Published: 13 Dec 2011
Abstract
We show that in a general \cal{N} = 1 supergravity with N \gg 1 scalar fields, an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking the superpotential and Kahler potential to be random functions, we construct a random matrix model for the Hessian matrix, which is well-approximated by the sum of a Wigner matrix and two Wishart matrices. We compute the eigenvalue spectrum analytically from the free convolution of the constituent spectra and find that in typical configurations, a significant fraction of the eigenvalues are negative. Building on the Tracy-Widom law governing fluctuations of extreme eigenvalues, we determine t...
Subjects
arXiv: High Energy Physics::Theory
free text keywords: High Energy Physics - Theory, Nuclear and High Energy Physics, Eigenvalues and eigenvectors, Hessian matrix, symbols.namesake, symbols, F-term, Matrix (mathematics), Physics, De Sitter universe, Quantum electrodynamics, Random matrix, Free convolution, Particle physics, Critical phenomena
Related Organizations
Funded by
NSF| Theoretical Particle Physics
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0757868
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Physics

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