Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Wasteland of Random Supergravities   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.

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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex