Character relations and replication identities in 2d Conformal Field Theory

TL;DR

This paper explores the replication identities of conformal characters in 2D CFT, offering insights into the Monstrous Moonshine Hauptmodul property and providing a framework for understanding these phenomena.

Contribution

It introduces a natural framework for interpreting replication identities in 2D CFT and connects them to the Monstrous Moonshine Hauptmodul property.

Findings

Replication identities relate conformal characters in 2D CFT.

Framework clarifies the physics behind Monstrous Moonshine.

Illustrations in simple cases demonstrate core ideas.

Abstract

We study replication identities satisfied by conformal characters of a 2D CFT, providing a natural framework for a physics interpretation of the famous Hauptmodul property of Monstrous Moonshine, and illustrate the underlying ideas in simple cases.