A representation of the string 2-group

TL;DR

This paper constructs a representation of the string 2-group on a 2-vector space using von Neumann algebras, aiming to categorify the spinor representation with implications for mathematical physics.

Contribution

It introduces a novel model for 2-vector spaces based on Morita bicategories of von Neumann algebras and represents the string 2-group on the hyperfinite type III_1 factor.

Findings

Representation of the string 2-group on a 2-vector space established.

Model connects categorification with von Neumann algebra theory.

Provides a foundation for further exploration in higher categorical quantum symmetries.

Abstract

We construct a representation of the string 2-group on a 2-vector space, aiming to establish it as the categorification of the spinor representation. Our model for 2-vector spaces is based on the Morita bicategory of von Neumann algebras, and we specifically represent the string 2-group on the hyperfinite type III_1 factor.