Convergence of Sewing Conformal Blocks

Abstract

In recent work, Damiolini-Gibney-Tarasca showed that for a $C_2$-cofinite rational CFT-type vertex operator algebra $\mathbb{V}$, sheaves of conformal blocks are locally free and satisfy the factorization property. In this article, we use analytic methods to prove that sewing conformal blocks is convergent, solving a conjecture proposed by Zhu and Huang.

65 pages. Final revision. To appear in Commun. Contemp. Math

Cited by in corpus (4)

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• Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case