Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras

Abstract

In this article, we develop a general technique for proving the uniqueness of holomorphic vertex operator algebras based on the orbifold construction and its "reverse" process. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge $24$ is uniquely determined by its weight one Lie algebra if the Lie algebra has the type $E_{6,3}{G}_{2,1}^3$, $A_{2,3}^6$ or $A_{5,3}{D}_{4,3}{A}_{1,1}^3$.

27 pages. arXiv admin note: text overlap with arXiv:1501.05094