Various semiclassical limits of torus conformal blocks

TL;DR

This paper explores four types of one-point torus conformal blocks in the large central charge limit, revealing their interconnections, algebraic contractions, and recursive representations relevant for semiclassical analysis.

Contribution

It introduces a unified framework linking global, light, heavy-light, and classical torus blocks, and formulates a c-recursive method for their semiclassical approximation.

Findings

Global, light, and heavy-light blocks are connected through algebraic contractions.

Different limits of conformal dimensions define distinct types of torus blocks.

A c-recursive representation for semiclassical approximation is developed.

Abstract

We study four types of one-point torus blocks arising in the large central charge regime. According to different limits of conformal dimensions we distinguish between the global block, the light block, the heavy-light block, and the linearized classical block. We show that they are not independent and connected to each other by various links. We find that the global, light, and heavy-light blocks correspond to three different contractions of the Virasoro algebra. Also, we formulate the c-recursive representation of the one-point torus blocks which is relevant in the semiclassical approximation.