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- Title
Convergence of sewing conformal blocks.
- Authors
Gui, Bin
- Abstract
In a recent work [On factorization and vector bundles of conformal blocks from vertex algebras, preprint (2019), arXiv:1909.04683], Damiolini et al. showed that for a C 2 -cofinite rational vertex operator algebra , sheaves of conformal blocks are locally free and satisfy the factorization property. In this paper, we prove that if is C 2 -cofinite, the sewing of conformal blocks is convergent. This proves a conjecture proposed by Zhu [Global vertex operators on Riemann surfaces, Commun. Math. Phys. 165(3) (1994) 485–531] and Huang [Some open problems in mathematical two-dimensional conformal field theory, preprint (2016), arXiv:1606.04493], generalizing previous results on the convergence of products, iterates, and traces (but not pseudo-traces) of vertex operators and intertwining operators in [Y. Zhu, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc. 9(1) (1996) 237–302; Y. Z. Huang, A theory of tensor products for module categories for a vertex operator algebra, IV, J. Pure Appl. Algebra 100(1–3) (1995) 173–216; Y. Z. Huang, Differential equations, duality and modular invariance, Commun. Contemp. Math. 7(05) (2005) 649–706; Y. Z. Huang, J. Lepowsky and L. Zhang, Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps, preprint (2011), arXiv:1110.1929] and on the convergence of projective factors related to the central charge of the Virasoro algebra in [Y. Z. Huang, Two-Dimensional Conformal Geometry and Vertex Operator Algebras, Vol. 148 (Springer Science & Business Media, 1997)].
- Subjects
CONFORMAL field theory; VECTOR bundles; CATEGORIES (Mathematics); CONFORMAL geometry; SEWING; VERTEX operator algebras; SHEAF theory
- Publication
Communications in Contemporary Mathematics, 2024, Vol 26, Issue 3, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199723500074