C_2-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras

Abstract

In this article, we give a sufficient and necessary condition for the $C_2$-cofiniteness of the 2-cycle permutation orbifold model $(V\otimes V{)}^{\sigma }$ for a $C_2$-cofinite vertex operator algebra and the 2-cycle permutation $\sigma$ of $V\otimes V$. As an application, we show that the 2-cycle permutation orbifold model of the simple Virasoro vertex operator algebra $L(c,0)$ of minimal central charge $c$ is $C_2$-cofinite.

24 pages, no figure, 1 appendix Some proofs are modified. To appear Communications in Mathematical Physics

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Cited by in corpus (5)

• Conformal blocks from vertex algebras and their connections on ${\overline{\mathcal{M}}}_{g,n}$
• $C_2$-cofiniteness of 2-cyclic permutation orbifold models
• 2-permutations of lattice vertex operator algebras: Higher rank
• Cyclic permutations of lattice vertex operator algebras
• The 3-permutation orbifold of a lattice vertex operator algebra