Orbifolds of lattice vertex algebras

To a positive-definite even lattice Q, one can associate the lattice vertex algebra V-Q, and any automorphism s of Q lifts to an automorphism of V-Q. In this paper, we investigate the orbifold vertex algebra V-Q(sigma), which consists of the elements of V-Q fixed under s, in the case when sigma has prime order. We describe explicitly the irreducible V-Q(sigma) -modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible V-Q(sigma) -modules. We consider in detail the cases when the order of sigma is 2 or 3, as well as the case of permutation orbifolds.