Abstract
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F| ≪ M susy or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log(P ) ∝ − N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
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Bachlechner, T.C. On Gaussian random supergravity. J. High Energ. Phys. 2014, 54 (2014). https://doi.org/10.1007/JHEP04(2014)054
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DOI: https://doi.org/10.1007/JHEP04(2014)054