Paper detail

On Gaussian Random Supergravity

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 $|F|\ll M_{\text{susy}}$ 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 $\log(P)\propto -N$. We argue that random supergravities lead to potentially interesting inflationary dynamics.