Differential equations and logarithmic intertwining operators for strongly graded vertex algebras

Abstract

We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable assumptions. Using these systems of differential equations, we verify the convergence and extension property needed in the logarithmic tensor category theory for such strongly graded generalized modules developed by Huang, Lepowsky and Zhang.

26 pages. For the sake of readability, I quote certain necessary technical definitions from earlier work of Y.-Z. Huang, J. Lepowsky and L. Zhang [arXiv:0710.2687, arXiv:1012.4193, arXiv:math/0609833]

References in corpus (3)

• Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra
• Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps
• Tensor products of strongly graded vertex algebras and their modules

Cited by in corpus (2)

• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• Vertex algebras associated to abelian current algebras