Franc Cameron, Mason Geoffrey
Department of Mathematics and Statistics, McMaster University, Hamilton, ON Canada.
Department of Mathematics, UC Santa Cruz, Santa Cruz, CA USA.
Res Number Theory. 2023;9(2):27. doi: 10.1007/s40993-023-00433-1. Epub 2023 Mar 29.
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 -adic Banach space replaces the traditional Hilbert space. We study some consequences of our axioms leading to the construction of various examples, including -adic commutative Banach rings and -adic versions of the Virasoro, Heisenberg, and the Moonshine module vertex operator algebras. Serre -adic modular forms occur naturally in some of these examples as limits of classical 1-point functions.
我们为非阿基米德二维玻色共形场论的一个手性部分假定公理，即一个顶点算子代数，其中(p)-adic 巴拿赫空间取代了传统的希尔伯特空间。我们研究公理的一些结果，从而构建各种示例，包括(p)-adic 交换巴拿赫环以及维拉索罗、海森堡和月光模顶点算子代数的(p)-adic 版本。塞尔(p)-adic 模形式在其中一些示例中自然地作为经典 1 点函数的极限出现。
