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

TL;DR

This paper establishes a criterion for the $C_2$-cofiniteness of 2-cycle permutation orbifold models of vertex operator algebras, and applies it to minimal Virasoro models, confirming their $C_2$-cofiniteness.

Contribution

It provides a necessary and sufficient condition for $C_2$-cofiniteness of permutation orbifold models and demonstrates this for minimal Virasoro vertex operator algebras.

Findings

Established a criterion for $C_2$-cofiniteness of orbifold models.

Proved that minimal Virasoro models' orbifolds are $C_2$-cofinite.

Enhanced understanding of orbifold vertex operator algebra properties.

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.