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arXiv · 2601.12017

Deformation rigidity of some simple affine VOAs

Andrew R. Linshaw·Fei Qi
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Abstract

In this paper, we prove that simple affine vertex operator algebras with positive integral levels admit only trivial first-order deformations. Therefore, the deformation rigidity conjecture of strongly rational vertex operator algebras holds for these cases. We also show that the same holds simple affine vertex operator algebra of $\mathfrak{sl}_2$ at the non-integral admissible level $-4/3$. Therefore, neither $C_2$-cofiniteness nor rationality is a necessary condition for deformation rigidity of VOAs. We conjecture that the same should hold for every simple affine VOA that does not coincide with the corresponding universal affine VOA.

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Andrew R. Linshaw, Fei Qi. 2026-01-17. Deformation rigidity of some simple affine VOAs. https://arxiv.org/abs/2601.12017

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