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arXiv · 2611.06201

$C_2$-Cofiniteness of Permutation Orbifolds I: Relative $C_1$ Descent

Yuhan Gu·Jiancai Sun
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Abstract

We establish a relative $C_1$-cofiniteness criterion for $C_2$-cofiniteness of finite group orbifolds. For permutation actions on a simple, self contragredient, $C_2$-cofinite vertex operator algebra of CFT type, it suffices to check a single relation for a derivative of the conformal vector in the Virasoro vertex operator algebra. This reduces the problem to a calculation depending only on the central charge and tensor degree. An exact calculation then proves cofiniteness for a family of nonsolvable permutation orbifolds without restricting the central charge.

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Yuhan Gu, Jiancai Sun. 2026-11-04. $C_2$-Cofiniteness of Permutation Orbifolds I: Relative $C_1$ Descent. https://arxiv.org/abs/2611.06201

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