The Clifford Algebra Bundle on Loop Space

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...

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Bibliographic Details
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
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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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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 transgressions of the second Stiefel-Whitney class and the first (fractional) Pontrjagin class of the manifold.
ISSN:1815-0659