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arXiv · 2206.09797

The stringor bundle

Peter Kristel·Matthias Ludewig·Konrad Waldorf
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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rigorously define the "stringor bundle", a higher differential geometric object anticipated by Stolz and Teichner in an unpublished preprint about 20 years ago.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.

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Peter Kristel, Matthias Ludewig, Konrad Waldorf. 2022-06-20. The stringor bundle. https://arxiv.org/abs/2206.09797

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