Classical conformal blocks and accessory parameters from isomonodromic deformations

Abstract

Abstract Classical conformal blocks appear in the large central charge limit of 2D Virasoro conformal blocks. In the AdS3 /CFT2 correspondence, they are related to classical bulk actions and used to calculate entanglement entropy and geodesic lengths. In this work, we discuss the identification of classical conformal blocks and the Painlevé VI action showing how isomonodromic deformations naturally appear in this context. We recover the accessory parameter expansion of Heun’s equation from the isomonodromic τ -function. We also discuss how the c = 1 expansion of the τ -function leads to a novel approach to calculate the 4-point classical conformal block.