Orbifolds of Lattice Vertex Algebras

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

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