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

Abstract

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

23 pages, no figure