Orbifold Vertex Operator Algebras and the Positivity Condition

Abstract

In this note we show that the irreducible twisted modules of a holomorphic, $C_2$-cofinite vertex operator algebra $V$ have $L_0$-weights at least as large as the smallest $L_0$-weight of $V$. Hence, if $V$ is of CFT-type, then the twisted $V$-modules are almost strictly positively graded. This in turn implies that the fixed-point vertex operator subalgebra $V^G$ for a finite, solvable group of automorphisms of $V$ almost satisfies the positivity condition. These and some further results are obtained by a careful analysis of Dong, Li and Mason's twisted modular invariance.

10 pages, LaTeX; comments welcome

References in corpus (2)

• A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications
• Twisted Modules over Lattice Vertex Algebras

Cited by in corpus (2)

• Schellekens' List and the Very Strange Formula
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices