Semi-classical Virasoro blocks: proof of exponentiation

TL;DR

This paper proves that Virasoro conformal blocks exponentiate in the large central charge and operator dimension limit using oscillator algebra techniques, providing new derivations of key results.

Contribution

It introduces a proof of Virasoro block exponentiation at large c using oscillator representations, and offers new derivations of standard conformal block results.

Findings

Virasoro blocks exponentiate at large c and h_i

Oscillator formulation effectively proves exponentiation

New derivations of conformal block properties

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.