Cite as: doi:10.26081/K6VG8G

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I will explore the idea that certain theories of gravity in Anti-de Sitter space
are dual to an average over an ensemble of quantum theories, rather than to a
specific quantum theory. I will consider the average over Narainâ€™s family of
two-dimensional conformal field theories which describe free bosons on a torus,
and compute the genus g partition function using the Siegel-Weil formula. The
result is a real analytic Eisenstein series which can be interpreted as the sum
over geometries in a theory of gravity. But the gravitational theory looks more
like a Chern-Simons theory than like Einstein gravity.
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