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arXiv · 2610.35749

Heavy Heisenberg Algebras, Zero Modes and Modularity

Darlayne Addabbo·Christoph A. Keller
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Abstract

It is known due to a result of Miyamoto that zero mode correlators of weight $1$ vectors of vertex operator algebras are quasi-modular forms, and that their generating series are Jacobi forms. In this article we generalize this to higher weight vectors. We consider weight 2 vectors that generate what we call heavy Heisenberg algebras. We prove that their zero mode correlators are a specific type of quasi-modular forms. As a consequence, they too can be summed up into a generating series with Jacobi-like modular transformation properties. As an application of our results, we sketch an argument that gives the asymptotic behavior of the dimensions of states of our VOAs.

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Darlayne Addabbo, Christoph A. Keller. 2026-10-26. Heavy Heisenberg Algebras, Zero Modes and Modularity. https://arxiv.org/abs/2610.35749

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