Nonabelian orbifolds and the boson-fermion correspondence

Abstract

For a positive integerl divisible by 8 there is a (bosonic) holomorphic vertex operator algebra (VOA) $$V_{\Gamma _l }$$ associated to the spin lattice Γ l . For a broad class of finite groupsG of automorphisms of $$V_{\Gamma _l }$$ we prove the existence and uniqueness of irreducibleg-twisted $$V_{\Gamma _l }$$ -modules and establish the modular-invariance of the partition functionsZ(g, h, τ) for commuting elements inG. In particular, for any finite group there are infinitely many holomorphic VOAs admittingG for which these properties hold. The proof is facilitated by a boson-fermion correspondence which gives a VOA isomorphism between $$V_{\Gamma _l }$$ and a certain fermionic construction, and which extends work of Frenkel and others.