NONABELIAN ORBIFOLDS AND THE BOSON-FERMION CORRESPONDENCE

For a positive integer l divisible by 8 there is a (bosonic) holomorphic vertex operator algebra (VOA) V(GAMMA)l associated to the spin lattice GAMMA(l). For a broad class of finite groups G of automorphisms of V(GAMMA)l we prove the existence and uniqueness of irreducible g-twisted V(GAMMA)l-modules and establish the modular-invariance of the partition functions Z(q, h, tau) for commuting elements in G. In particular, for any finite group there are infinitely many holomorphic VOAs admitting G 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.