On twisted representations of vertex algebras

Abstract

In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is the construction of a very large family of representations for the vertex superalgebra $\goth V_\Lambda$ corresponding to an integer lattice $\Lambda$. For an automorphism $\^\sigma:\goth V_\Lambda\to\goth V_\Lambda$ coming from a finite order automorphism $\sigma:\Lambda \to \Lambda$ we define a category $\cal O_{\^\sigma}$ of twisted representations of $\goth V_\Lambda$ and show that this category is semisimple with finitely many isomorphism classes of simple objects.