Non-Abelian Orbifolds of Lattice Vertex Operator Algebras

TL;DR

This paper develops a method to construct and analyze orbifolds of lattice vertex operator algebras with non-Abelian automorphism groups, leading to the creation of over fifty new holomorphic VOAs with minimal light states.

Contribution

It introduces a novel construction of twisted modules for non-Abelian automorphisms and uses them to generate new holomorphic VOAs from extremal lattices.

Findings

Constructed twisted modules for non-Abelian automorphisms.

Computed characters and modular properties of fixed point VOAs.

Generated over fifty new holomorphic VOAs with few light states.

Abstract

We construct orbifolds of holomorphic lattice Vertex Operator Algebras for non-Abelian finite automorphism groups $G$. To this end, we construct twisted modules for automorphisms $g$ together with the projective representation of the centralizer of $g$ on the twisted module. This allows us to extract the irreducible modules of the fixed point VOA $V^G$, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to $V^G$. Applying these methods to extremal lattices in $d=48$ and $d=72$, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states.