On factorization and vector bundles of conformal blocks from vertex algebras

2019/09/10 by Chiara Damiolini, Damiolini, Chiara, Angela Gibney +3 · 4 citations
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1909.04683

Abstract

Representations of vertex operator algebras define sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity conditions, we prove that such sheaves satisfy the factorization conjecture and consequently are vector bundles. Factorization is essential to a recursive formulation of invariants, like ranks and Chern classes, and to produce new constructions of rational conformal field theories and cohomological field theories.

Cited by

• Non-Equivalence of Smooth and Nodal Conformal Block Functors in Logarithmic CFT
• Reflection Equivariance and the Heisenberg Picture for Spaces of Conformal Blocks
• Modular functors from conformal blocks of rational vertex operator algebras
• Positivity of coinvariant divisors on M_0,n and the parafermions

Related

• Applications of the factorization theorem of conformal blocks to vertex operator algebras
• Factorization presentations
• Vertex algebras of CohFT-type
• Modular functors from conformal blocks of rational vertex operator algebras
• Vertex Algebras and Costello-Gwilliam Factorization Algebras