English

The stringor bundle

Algebraic Topology 2024-04-24 v3 Mathematical Physics Differential Geometry math.MP Operator Algebras

Abstract

We set up a framework of 2-Hilbert bundles, which allows to rigorously define the "stringor bundle", a higher differential geometric object anticipated by Stolz and Teichner in an unpublished preprint about 20 years ago. Our framework includes an associated bundle construction, allowing us to associate a 2-Hilbert bundle with a principal 2-bundle and a unitary representation of its structure 2-group. We prove that the Stolz-Teichner stringor bundle is canonically isomorphic to the 2-Hilbert bundle obtained from applying our associated bundle construction to a string structure on a manifold and the stringor representation of the string 2-group that we discovered in earlier work. This establishes a perfect analogy to spin manifolds, representations of the spin groups, and spinor bundles.

Keywords

Cite

@article{arxiv.2206.09797,
  title  = {The stringor bundle},
  author = {Peter Kristel and Matthias Ludewig and Konrad Waldorf},
  journal= {arXiv preprint arXiv:2206.09797},
  year   = {2024}
}

Comments

68 pages. In v2 the title has been changed. The original title was "A representation of the string 2-group"; under this title a new paper appeared (2308.05139) containing the content of section 3, which was then removed here. v3 is an improved rewritten version

R2 v1 2026-06-24T11:57:19.878Z