Construction and Classification of Holomorphic Vertex Operator Algebras

TL;DR

This paper develops an orbifold theory for holomorphic vertex operator algebras, proves Schellekens' classification as a theorem, and constructs new examples of such algebras at central charge 24.

Contribution

It introduces an orbifold framework for finite cyclic group actions on VOAs, proving Schellekens' classification as a theorem and constructing new VOAs via lattice orbifolds.

Findings

Orbifold theory for cyclic group actions on VOAs

Schellekens' classification proven as a theorem

New holomorphic VOAs constructed as lattice orbifolds

Abstract

We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens' classification of $V_1$-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.