$C_2$-cofiniteness of 2-cyclic permutation orbifold models

Abstract

In this article, we consider permutation orbifold models of $C_2$-cofinite vertex operator algebras of CFT type. We show the $C_2$-cofiniteness of the 2-cyclic permutation orbifold model $(V\otimes V{)}^{S_2}$ for an arbitrary $C_2$-cofinite simple vertex operator algebra $V$ of CFT type. We also give a proof of the $C_2$-cofiniteness of a ${\mathbb{Z}}_2$-orbifold model $V_L^{+}$ of the lattice vertex operator algebra $V_L$ associated with a rank one positive definite even lattice $L$ by using our result and the $C_2$-cofiniteness of $V_L$.

25 pages, no figure, some typo are corrected

References in corpus (4)

• The kernel of the modular representation and the Galois action in RCFT
• Permutation orbifolds
• Rationality, quasirationality and finite W-algebras
• C_2-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras

Cited by in corpus (2)

• Conformal blocks from vertex algebras and their connections on ${\overline{\mathcal{M}}}_{g,n}$
• Permutation Orbifolds of the Heisenberg Vertex Algebra $\mathcal{H}(3)$