Quasi-modular forms and trace functions associated to free boson and lattice vertex operator algebras

2000/04/20 by Chongying Dong, Dong, Chongying, Geoffrey Mason +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0004132

Latex 18 pages

arxiv created 2000/04/20 · openalex publication_date 2000/04/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study graded traces of vectors in free bosonic vertex operator algebras and lattice vertex operator algebras. We show in particular that trace functions in these two theories always have the shape f(q)/η(q)^d where f(q) is quasi-modular in the case of d free bosons, and modular (i.e., a sum of holomorphic modular forms of various weights) in the case of theories based on a lattice L of rank d. We also show how spherical harmonic polynomials with respect to L are related to primary fields in lattice theories.

Citations

• Local systems of vertex operators, vertex superalgebras and modules

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