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

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.

Automated summary

The study focuses on the origin of the effective theory of stress tensor exchanges based on reparametrization modes for computing Virasoro identity blocks efficiently. A derivation of the governing Alekseev-Shatashvili action for these modes is provided, along with an interpretation as the generating functional of stress tensor correlations. The natural emergence of the prescribed rules for computing Virasoro identity blocks is demonstrated when evaluating Feynman diagrams associated with stress tensor exchanges. Additionally, brief comments are made on the connection of these results to gravitational theories and holography.