Semi-classical Virasoro blocks: proof of exponentiation

Abstract: Virasoro conformal blocks are expected to exponentiate in the limit of large central charge $c$ and large operator dimensions $h_i$, with the ratios $h_i/c$ held fixed. We prove this by employing the oscillator formulation of the Virasoro algebra and its representations. The techniques developed are then used to provide new derivations of some standard results on conformal blocks.