Codes, Vertex Operators and Topological Modular Forms

TL;DR

This paper establishes a novel connection between topological modular forms and vertex operator algebra representations derived from lattices, motivated by the arithmetic Whitehead tower of orthogonal groups, highlighting the role of codes in representation theory.

Contribution

It introduces a new link between topological modular forms and lattice-based vertex operator algebra representations, inspired by the Whitehead tower and codes.

Findings

Identifies a new relationship between topological modular forms and vertex operator algebras.

Highlights the role of codes in the representation theory of vertex operator algebras.

Provides a construction motivated by the arithmetic Whitehead tower of orthogonal groups.

Abstract

We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups. The tower discloses the role of codes in representation theory.