Classical conformal blocks and accessory parameters from isomonodromic deformations

Classical conformal blocks appear in the large central charge limit of 2D Vira-soro conformal blocks. In the AdS(3)/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 Painleve VI action showing how isomonodromic deformations naturally appear in this context. We recover the accessory parameter expansion of Heun's equation from the isomonodromic tau-function. We also discuss how the c = 1 expansion of the tau-function leads to a novel approach to calculate the 4-point classical conformal block.