The Clifford Algebra Bundle on Loop Space

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Ludewig, Matthias
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212103
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Clifford Algebra Bundle on Loop Space. Matthias Ludewig. SIGMA 20 (2024), 020, 27 pages

We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop space. We show that this bundle is in general non-trivial, more precisely that its triviality is obstructed by the tran...