[Submitted on 12 Jun 2026]

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Abstract:We prove that, for a classically free vertex algebra, the $C_2$-algebra is naturally isomorphic to the associated graded algebra of Zhu's algebra. As an application, we show that non-trivial holomorphic VOAs of CFT type are not classically free. This includes the affine vertex operator algebra of $E_8$ at level one, as well as the Moonshine VOA.

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From: Xianlong Zeng [view email]
[v1] Fri, 12 Jun 2026 12:43:20 UTC (19 KB)

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