The Wasteland of Random Supergravities
arXiv:1112.3034 · doi:10.1007/JHEP03(2012)102
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 the probability P of a large fluctuation in which all the eigenvalues become positive. Strong eigenvalue repulsion makes this extremely unlikely: we find P \propto exp(-c N^p), with c, p being constants. For generic critical points we find p \approx 1.5, while for approximately-supersymmetric critical points, p \approx 1.3. Our results have significant implications for the counting of de Sitter vacua in string theory, but the number of vacua remains vast.
39 pages, 9 figures; v2: fixed typos, added refs and clarifications
References in corpus (7)
- Flux Compactification
- Large Deviations of Extreme Eigenvalues of Random Matrices
- Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
- Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
- Cosmology From Random Multifield Potentials
- Universality for mathematical and physical systems
- A simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix
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