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

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

2010-05-11

arxiv.org/abs/1005.1767v2

Mathematics

Quantum Algebra

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

Scientific paper

10.1007/s00220-011-1209-x

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.

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