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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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Cite

BibTeXRIS
BibTeX
@misc{addabbo2026heavy,
  title = {{Heavy Heisenberg Algebras, Zero Modes and Modularity}},
  author = {Darlayne Addabbo and Christoph A. Keller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35749},
  eprint = {2610.35749},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35749},
}
RIS
TY  - UNPB
TI  - Heavy Heisenberg Algebras, Zero Modes and Modularity
AU  - Darlayne Addabbo
AU  - Christoph A. Keller
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35749
UR  - https://arxiv.org/abs/2610.35749
AB  - 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.
ER  -