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SUMMARY:The Wasteland of Random Supergravities - McAllister\, L (Cornell U
 niversity)
DTSTART:20120627T091000Z
DTEND:20120627T094500Z
UID:TALK38703@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We show that in a general N=1 supergravity with N >> 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 mat
 rix\, which is well-approximated by the sum of a Wigner matrix and two Wis
 hart matrices. We compute the eigenvalue spectrum analytically from the fr
 ee convolution of the constituent spectra and find that in typical configu
 rations\, a significant fraction of the eigenvalues are negative. Using Co
 ulomb gas techniques\, we then determine the probability P of a large fluc
 tuation in which all the eigenvalues become positive. Strong eigenvalue re
 pulsion makes this extremely unlikely: we find P propto exp(-c N^2)\, with
  c a constant\, for generic critical points. Our results have significant 
 implications for the counting of de Sitter vacua in string theory\, but th
 e number of vacua remains vast. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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