From global to heavy-light: 5-point conformal blocks

TL;DR

This paper explores the relationships between different regimes of Virasoro conformal blocks at large central charge, focusing on 5-point functions, and demonstrates how to derive heavy-light blocks from global blocks.

Contribution

It introduces a method to relate global and heavy-light 5-point conformal blocks, extending previous work to more complex configurations.

Findings

Derived 5-point global conformal blocks using projector and Casimir techniques.

Established the connection between global and heavy-light limits for 5-point blocks.

Reproduced classical heavy-light blocks from global blocks using the monodromy method.

Abstract

We consider Virasoro conformal blocks in the large central charge limit. There are different regimes depending on the behavior of the conformal dimensions. The most simple regime is reduced to the global sl(2, C) conformal blocks while the most complicated one is known as the classical conformal blocks. Recently, Fitzpatrick, Kaplan, and Walters showed that the two regimes are related through the intermediate stage of the so-called heavy-light semiclassical limit. We study this idea in the particular case of the 5-point conformal block. To find the 5-point global block we use the projector technique and the Casimir operator approach. Furthermore, we discuss the relation between the global and the heavy-light limits and construct the heavy-light block from the global block. In this way we reproduce our previous results for the 5-point perturbative classical block obtained by means of the monodromy method.