Global torus blocks in the necklace channel

TL;DR

This paper investigates global conformal blocks on the torus in a specific channel, providing explicit functions under certain conditions and confirming they satisfy the Casimir equations.

Contribution

It explicitly derives multi-point conformal blocks in the necklace channel and verifies their compliance with Casimir equations.

Findings

Explicit multi-point blocks derived under special conditions

Verification that blocks satisfy Casimir equations

Enhanced understanding of torus conformal blocks in the necklace channel

Abstract

We continue studying of global conformal blocks on the torus in a special (necklace) channel. Functions of such multi-point blocks are explicitly found under special conditions on the blocks' conformal dimensions. We have verified that these blocks satisfy the Casimir equations, which were derived in previous studies.