Virasoro blocks and the reparametrization formalism

TL;DR

This paper develops a formal theoretical framework for an effective theory that computes Virasoro identity blocks at large central charge, using conformal geometry and Feynman diagrams, and extends it to generic Virasoro blocks.

Contribution

It reformulates an effective theory for Virasoro blocks in terms of standard concepts like conformal geometry and Feynman diagrams, providing a rigorous foundation and extension.

Findings

Formalizes the effective theory using conformal geometry and Feynman diagrams.

Shows the bilocal vertex operator generates stress tensor insertions.

Proposes an extension for computing generic Virasoro blocks.

Abstract

An effective theory designed to compute Virasoro identity blocks at large central charge, expressed in terms of the propagation of a reparametrization/shadow mode between bilocal vertices, was recently put forward. In this paper I provide the formal theoretical framework underlying this effective theory by reformulating it in terms of standard concepts : conformal geometry, generating functionals and Feynman diagrams. A key ingredient to this formalism is the bilocal vertex operator, or reparametrized two-point function, which is shown to generate arbitrary stress tensor insertions into a two-point function of reference. I also suggest an extension of the formalism designed to compute generic Virasoro blocks.