We construct a representation of the string 2-group on a 2-vector space, namely on the hyperfinite type III_1 von Neumann algebra. We prove that associating this representation to the frame bundle of a string manifold yields the stringor bundle of Stolz-Teichner, thus establishing a perfect analogy to spin manifolds, representations of the spin groups, and spinor bundles.
- Pub Date:
- June 2022
- Mathematics - Algebraic Topology;
- Mathematical Physics;
- Mathematics - Differential Geometry;
- Mathematics - Operator Algebras
- 68 pages. In v2 the title has been changed. The original title was "A representation of the string 2-group"