p-adic vertex operator algebras

TL;DR

This paper introduces axioms for p-adic vertex operator algebras, extending conformal field theory into the nonarchimedean setting and constructing examples related to p-adic modular forms.

Contribution

It formulates axioms for p-adic VOAs and constructs examples including p-adic Virasoro, Heisenberg, and Moonshine modules, connecting to p-adic modular forms.

Findings

Construction of p-adic vertex operator algebras

Examples of p-adic Virasoro, Heisenberg, Moonshine modules

Connection to Serre p-adic modular forms

Abstract

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.