p-adic vertex operator algebras

We postulate axioms for a chiral half of a nonarchimedean 2-dimensional bosonic conformal field theory, that is, a vertex operator algebra in which a p -adic Banach space replaces the traditional Hilbert space. We study some consequences of our axioms leading to the construction of various examples,...

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Bibliographic Details
Published in:Research in number theory 2023, Vol.9 (2), p.27-27, Article 27
Main Authors: Franc, Cameron, Mason, Geoffrey
Format: Article
Language:English
Subjects:
Algebra
Axioms
Banach spaces
Field theory
Hilbert space
Mathematical analysis
Mathematics
Mathematics and Statistics
Number Theory
Operators (mathematics)
Rings (mathematics)
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Summary:We postulate axioms for a chiral half of a nonarchimedean 2-dimensional bosonic conformal field theory, that is, a vertex operator algebra in which a p -adic Banach space replaces the traditional Hilbert space. We study some consequences of our axioms leading to the construction of various examples, including p -adic commutative Banach rings and p -adic versions of the Virasoro, Heisenberg, and the Moonshine module vertex operator algebras. Serre p -adic modular forms occur naturally in some of these examples as limits of classical 1-point functions.
ISSN:2522-0160
2363-9555
2363-9555
DOI:10.1007/s40993-023-00433-1