Characters in p-adic Heisenberg and Lattice Vertex Operator Algebras

TL;DR

This paper investigates characters in p-adic vertex operator algebras, revealing that their images include infinitely many non-classical p-adic modular forms not seen in classical algebraic character maps.

Contribution

It demonstrates the existence of non-classical p-adic modular forms within the character images of p-adic Heisenberg and lattice vertex operator algebras.

Findings

Character maps include infinitely many non-classical p-adic modular forms.

These forms are not contained in the classical algebraic character map.

The study advances understanding of p-adic VOA character theory.

Abstract

We study characters of states in $p$-adic vertex operator algebras. In particular, we show that the image of the character map for both the $p$-adic Heisenberg and $p$-adic lattice vertex operator algebras contain infinitely-many non-classical $p$-adic modular forms which are not contained in the image of the algebraic character map.