3-State Potts model and automorphism of vertex operator algebra of order 3

TL;DR

This paper constructs an automorphism of order 3 in vertex operator algebras using a sub VOA related to the 3-state Potts model, linking it to the Monster group in the moonshine VOA.

Contribution

It introduces a new automorphism of order 3 in VOAs based on the 3-state Potts model and connects it to the Monster group's 3A element.

Findings

Automorphism of order 3 constructed using 3-state Potts model sub VOA.

Automorphism corresponds to a 3A element in the Monster group.

Applicable to the moonshine VOA $V^{\natural}$.

Abstract

We define an automorphism of VOA of order 3 by using a sub VOA isomorphic to a direct sum of 3-state Potts models $L(\ff,0)$ and an its module $L(\ff,3)$. This automorphism is a 3A element of the monster simple group if $V$ is the moonshine VOA $V^{\natural}$.