Year: 2023
Type: preprint
Abstract: We give a construction of the spinor bundle of the loop space of a string manifold together with its fusion product, inspired by ideas from Stolz and Teichner. The spinor bundle is a super bimodule bundle for a bundle of Clifford von Neumann algebras over the free path space, and the fusion product is defined using Connes fusion of such bimodules. As the main result, we prove that a spinor bundle with fusion product on a manifold X exists if and only X admits a string structure.
Source: arXiv (Cornell University)
Author: Ludewig, Matthias
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4377864430