Orbifolds of lattice vertex algebras under an isometry of order two

Abstract

Every isometry $\sigma$ of a positive-definite even lattice $Q$ can be lifted to an automorphism of the lattice vertex algebra $V_Q$. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the $\sigma$-invariant subalgebra $V_Q^{\sigma }$ of $V_Q$, known as an orbifold. In the case when $\sigma$ is an isometry of $Q$ of order two, we classify the irreducible modules of the orbifold vertex algebra $V_Q^{\sigma }$ and identify them as submodules of twisted or untwisted $V_Q$-modules. The examples where $Q$ is a root lattice and $\sigma$ is a Dynkin diagram automorphism are presented in detail.

27 pages; v2 typos fixed and a reference added

References in corpus (8)

• Vertex Algebras and Algebraic Curves
• Modular invariance of trace functions in orbifold theory
• C_2-cofiniteness of cyclic-orbifold models
• Affine orbifolds and rational conformal field theory extensions of W_{1+infinity}
• Representations of vertex operator algebra V_L^+ for rank one lattice L
• W-Constraints for the Total Descendant Potential of a Simple Singularity
• Rationality of vertex operator algebra V_L^+: higher rank
• Flatness and Semi-Rigidity of Vertex Operator Algebras

Cited by in corpus (6)

• Twisted logarithmic modules of lattice vertex algebras
• Representations of Twisted Toroidal Lie Algebras from Twisted Modules over Vertex Algebras
• Orbifolds of Lattice Vertex Algebras
• 2-permutations of lattice vertex operator algebras: Higher rank
• The 3-permutation orbifold of a lattice vertex operator algebra
• Quantum dimensions and fusion products for irreducible V_Q^s-modules, where s is an isometry of Q with s^2=1