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Towards a 1/c Expansion in 2d Conformal Field Theory

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I will describe progress in deriving 3d gravity directly from 2d conformal field theory at large central charge 'c'. In a large class of CFTs, using general arguments like modular invariance, crossing symmetry, and the OPE expansion, the spectrum, the entanglement entropy, and certain partition functions can be computed to leading order in a 1/c expansion. The results agree with universal features of 3d gravity required by black hole thermodynamics and the Ryu-Takayanagi formula; furthermore, the relevant 3d geometries appear automatically from CFT calculations in this regime.