Analytic Conformal Blocks of $C_2$-cofinite Vertex Operator Algebras II: Convergence of Sewing and Higher Genus Pseudo-$q$-traces

Bin Gui, Hao Zhang

Let $\mathbb{V}={⨁}_{n\in \mathbb{N}}\mathbb{V}(n)$ be a $C_2$-cofinite vertex operator algebra. We prove the convergence of Segal's sewing of conformal blocks associated to anal…