article · Compositio Mathematica · 2024
Connes fusion of spinors on loop space
Cited by 1Open access
Abstract
The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of two-dimensional sigma models as the bundle of states over the configuration space of the superstring. We construct a product on this bundle that covers the fusion of loops, i.e. the merging of two loops along a common segment. For this purpose, we exhibit it as a bundle of bimodules over a certain von Neumann algebra bundle, and realize our product fibrewise using the Connes fusion of von Neumann bimodules. Our main technique is to establish novel relations between string structures, loop fusion, and the Connes fusion of Fock spaces. The fusion product on the spinor bundle on loop space was proposed by Stolz and Teichner as part of a programme to explore the relation between generalized cohomology theories, functorial field theories, and index theory. It is related to the pair of pants worldsheet of the superstring, to the extension of the corresponding smooth functorial field theory down to the point, and to a higher-categorical bundle on the underlying string manifold, the stringor bundle.
Cite this paper
Kristel, P., & Waldorf, K. (2024). Connes fusion of spinors on loop space. Compositio Mathematica, 160(7), 1596–1650. https://doi.org/10.1112/s0010437x24007188
Kristel, P., and Konrad Waldorf. “Connes fusion of spinors on loop space.” Compositio Mathematica, vol. 160, no. 7, 2024, pp. 1596–650, https://doi.org/10.1112/s0010437x24007188.
Kristel, P., and Konrad Waldorf. 2024. “Connes fusion of spinors on loop space.” Compositio Mathematica 160 (7): 1596–650. https://doi.org/10.1112/s0010437x24007188.
Kristel, P. and Waldorf, K. (2024) ‘Connes fusion of spinors on loop space’, Compositio Mathematica, 160(7), pp. 1596–1650. Available at: https://doi.org/10.1112/s0010437x24007188.
@article{kristel2024connes,
title = {{Connes fusion of spinors on loop space}},
author = {Kristel, P. and Waldorf, Konrad},
journal = {Compositio Mathematica},
volume = {160},
number = {7},
pages = {1596--1650},
year = {2024},
doi = {10.1112/s0010437x24007188}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.