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Title:
The Siegel-Weil Formula and Quantum Gravity as an Average
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Abstract:
I will explore the idea that certain theories of gravity are not traditional quantum theories, but are instead averages over ensembles of quantum theories. I will consider the average over free boson conformal field theories in two dimensions, 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 certain exotic - but in a sense exactly solvable - theory of quantum gravity. The techniques used are similar to those used to study high dimensional sphere packing by averaging over spaces of lattices, suggesting an analogy between semi-classical gravity and a theory of random lattices (or sphere packings) in high dimensions.
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