Extensions of tensor products of ${\mathbb Z}_p$-orbifold models of the lattice vertex operator algebra $V_{\sqrt{2}A_{p-1}}$

TL;DR

This paper investigates extensions of tensor products of orbifold models derived from lattice vertex operator algebras, providing criteria for when all irreducible modules are simple currents, with implications for the structure of these models.

Contribution

It introduces a new criterion for extensions of tensor products of orbifold models to have all irreducible modules as simple currents.

Findings

Established a criterion for simple current modules in extended orbifold models

Analyzed the structure of extensions of tensor products of lattice VOA orbifolds

Provided conditions under which all irreducible modules are simple currents

Abstract

Let $p$ be an odd prime and let $\widehat{\sigma}$ be an order $p$ automorphism of $V_{\sqrt{2}A_{p-1}}$ which is a lift of a $p$-cycle in the Weyl group ${\rm Weyl}(A_{p-1})\cong {\mathfrak S}_p$. We study a certain extension $V$ of a tensor product of finitely many copies of the orbifold model $V_{\sqrt{2}A_{p-1}}^{\langle \widehat{\sigma} \rangle}$ and give a criterion for $V$ that every irreducible $V$-module is a simple current.