Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-12-13
Physics
High Energy Physics
High Energy Physics - Theory
39 pages, 9 figures; v2: fixed typos, added refs and clarifications
Scientific paper
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.
Marsh David
McAllister Liam
Wrase Timm
No associations
LandOfFree
The Wasteland of Random Supergravities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Wasteland of Random Supergravities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Wasteland of Random Supergravities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-223973