Orbifolds of Lattice Vertex Algebras

To a positive-definite even lattice \(Q\), one can associate the lattice vertex algebra \(V_Q\), and any automorphism \(\sigma\) 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 \(\sigma\), 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.