Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras

TL;DR

This paper investigates the automorphism groups of cyclic orbifolds of lattice vertex operator algebras, revealing conditions under which extra automorphisms arise beyond those induced by the lattice structure.

Contribution

It characterizes when cyclic orbifolds have additional automorphisms, linking this to Construction B lattices and coinvariant lattices of the Leech lattice.

Findings

Extra automorphisms occur if the lattice is from Construction B or related to the Leech lattice.

Automorphisms are characterized by lattice construction and isometry properties.

Provides criteria for the existence of non-lattice-induced automorphisms in orbifolds.

Abstract

In this article, we study the automorphism group of the cyclic orbifold of a vertex operator algebra associated with a rootless even lattice for a lift of a fixed-point free isometry of odd prime order $p$. We prove that such a cyclic orbifold contains extra automorphisms, not induced from automorphisms of the lattice vertex operator algebra, if and only if the rootless even lattice can be constructed by Construction B from a code over $\mathbb{Z}_p$ or is isometric to the coinvariant lattice of the Leech lattice associated with a certain isometry of order $p$.