Ising vectors and automorphism groups of commutant subalgebras related to root systems

Abstract

In this article we study and obtain a classification of Ising vectors in vertex operator algebras (VOAs) associated to binary codes and \(\sqrt{2}\) times root lattices, where an Ising vector is a conformal vector with central charge 1/2 generating a simple Virasoro sub-VOA. Then we apply our results to study certain commutant subalgebras related to root systems. We completely classify all Ising vectors in such commutant subalgebras and determine their full automorphism groups.