2023/05/24 by Yi-Zhi Huang, Huang, Yi-Zhi · 1 citation
Computer Science · Mathematics · #17B69 #32N10 #81T40 #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2305.15152
openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let V be a C2-cofinite vertex operator algebra without nonzero elements of negative weights. We prove the conjecture that the spaces spanned by analytic extensions of pseudo-q-traces (q=e2πiτ) shifted by -(c)/(24) of products of geometrically-modified (logarithmic) intertwining operators among grading-restricted generalized V-modules are invariant under modular transformations. The convergence and analytic extension result needed to formulate this conjecture and some consequences on such shifted pseudo-q-traces were proved by Fiordalisi in [F1] and [F2] using the method developed in [H2]. The method that we use to prove this conjecture is based on the theory of the associative algebras AN(V) for N∈ ℕ, their graded modules and their bimodules introduced and studied by the author in [H8] and [H9]. This modular invariance result gives a construction of C2-cofinite genus-one logarithmic conformal field theories from the corresponding genus-zero logarithmic conformal field theories.