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Exceptional Seminar Akinori Tanaka (RIKEN, Wako, JAPAN)
room Norfork G.01
In 2007, it was conjectured by E.Witten that the chiral part of the partition function of 3d pure AdS Einstein gravity in quantum regime coincides with so-called modular J-function, a partition function of certain holomorphic CFT, called "monster CFT" considered by I. B Frenkel, J. Lepowsky and A. Meurman in the context of monstrous moonshine. We tried to calculate the partition function for the 3d pure AdS Einstein gravity directly by utilizing recently developed localization techniques.Based on some plausible assumptions, we arrived at CFT interpretations.For quantum gravity regime which corresponds to c=24, we get J-function.For semiclassical regime which corresponds c>>1, our partition function decomposes to Virasoro characters, and we derive Cardy formula. If possible, I will comment on application to quantum higher spin gravity.This talk is based on 1504.05991 and 1510.02142.