Conformal Blocks Beyond the Semi-Classical Limit

Abstract

Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT. Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT2, which encapsulate quantum gravitational effects in AdS3. At infinite central charge c, the Virasoro vacuum block provides an avatar of the black hole information paradox in the form of periodic Euclidean-time singularities that must be resolved at finite c. We compute Virasoro blocks in the heavy-light, large c limit, extending our previous results by determining perturbative 1/c corrections. We obtain explicit closed-form expressions for both the `semi-classical' $h_L^2 / c^2$ and `quantum' $h_L / c^2$ corrections to the vacuum block, and we provide integral formulas for general Virasoro blocks. We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using `geodesic Witten diagrams'. We expect that only non-perturbative corrections in 1/c can resolve the singularities associated with the information paradox.Comment: 24+7 pages, 5 figures; v2 fixed typo in eq 2.22, added refs; v3 fixed typo