Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges

TL;DR

This paper derives an effective theory for stress tensor exchanges in 2D CFT using reparametrization modes, connecting it to conformal transformations, Feynman diagrams, and holography, enhancing computational methods for Virasoro blocks.

Contribution

It provides a derivation of the Alekseev--Shatashvili action for reparametrization modes and links it to stress tensor correlations and Virasoro identity blocks in 2D CFT.

Findings

Derived the nonlinear Alekseev--Shatashvili action for reparametrization modes.

Showed how to compute Virasoro identity blocks using stress tensor exchange diagrams.

Connected the effective theory to gravitational and holographic frameworks.

Abstract

We study the origin of the recently proposed effective theory of stress tensor exchanges based on reparametrization modes, that has been used to efficiently compute Virasoro identity blocks at large central charge. We first provide a derivation of the nonlinear Alekseev--Shatashvili action governing these reparametrization modes, and argue that it should be interpreted as the generating functional of stress tensor correlations on manifolds related to the plane by conformal transformations. In addition, we demonstrate that the rules previously prescribed with the reparametrization formalism for computing Virasoro identity blocks naturally emerge when evaluating Feynman diagrams associated with stress tensor exchanges between pairs of external primary operators. We make a few comments on the connection of these results to gravitational theories and holography.