Abstract

I will discuss the mass spectrum of four-dimensional {
l N}=1 supergravity in which the Khler potential and superpotential are taken to be random functions of N chiral superfields. For both supersymmetric and non-supersymmetric critical points, the ensemble of Hessian matrices can be efficiently studied through the Coulomb gas formulation of Random Matrix Theory. At large N, the supersymmetric AdS vacua have a very peculiar spectrum which typically includes many BF-allowed tachyons, and I will briefly discuss the prospects of obtaining metastable de Sitter vacua from an uplift of a supersymmetric AdS vacuum. An exponentially small fraction de Sitter critical points with spontaneously broken supersymmetry are metastable vacua, and I will discuss how the Coulomb gas formulation can be used to find the joint probability distribution of the masses, the fraction of critical points which are vacua, and the spectrum of the vacua. I will conclude by b riefly discussing some cosmological consequences of these results.