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High Energy Physics - Theory, hep-th
Abstract:
We evaluate the partition function of three dimensional theories of gravity
in the quantum regime, where the AdS radius is Planck scale and the central
charge is of order one. The contribution from the AdS vacuum sector can - with
certain assumptions - be computed and equals the vacuum character of a minimal
model CFT. The torus partition function is given by a sum over geometries which
is finite and computable. For generic values of Newton's constant G and the AdS
radius L the result has no Hilbert space interpretation, but in certain cases
it agrees with the partition function of a known CFT. For example, the
partition function of pure Einstein gravity with G=3L equals that of the Ising
model, providing evidence that these theories are dual. We also present
somewhat weaker evidence that the 3-state and tricritical Potts models are dual
to pure higher spin theories of gravity based on SL(3) and E_6, respectively.
