Mon, Dec 9, 2013, 2:30 pm to 3:30 pm
PCTS Seminar Room
I will present results on the statistics of metastable vacua in string theory. Standard counts of string vacua, including the celebrated estimate of >10^500 flux vacua in type IIB string theory, do not incorporate the constraint of metastability, and therefore effectively count the combined number of maxima, minima, and unstable saddle points. We show that in general N=1 supergravity theories with N >> 1 scalar fields, metastability is an extremely strong constraint: the probability that a generic critical point is a metastable minimum, rather than an unstable saddle, is exp(-c N^2), for a constant c. Even approximately-supersymmetric critical points are overwhelmingly likely to be unstable, with positivity probability exp(-d N). We arrive at these results by deriving a random matrix model for the Hessian in supergravity and computing its spectrum analytically. Our findings have significant implications for the counting of de Sitter vacua in string theory, but the number of vacua remains vast.