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String connections and Chern-Simons theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 05 Mar 2013Embargo end date: 01 Jan 2009Publisher:American Mathematical Society (AMS)Journal:Transactions of the American Mathematical Society, volume 365, pages 4,393-4,432 (issn: 0002-9947, eissn: 1088-6850,

Authors: Konrad Waldorf; Konrad Waldorf;

doi: 10.1090/s0002-9947-2013-05816-3 , 10.48550/arxiv.0906.0117

arXiv: http://arxiv.org/abs/0906.0117

String connections and Chern-Simons theory

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Abstract

We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string connections: it enables us to prove that every string structure admits a string connection and that the possible choices form an affine space. Further we discover a new relation between string connections, 3-forms on the base manifold, and degree three differential cohomology. We also discuss in detail the relation between our formulation of string connections and the original version of Stolz and Teichner.

55 pages; v2: new section with a better treatment of the relation to string connections of Stolz-Teichner, minor changes otherwise; v3: some newest developments referenced, minor changes; v4 comes with typos corrected and is the final and published version

Related Organizations

University of California, Berkeley
United States
University of Regensburg
Germany

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics, Algebraic Topology (math.AT), 53C08 (Primary) 57R56, 57R15 (Secondary), Mathematics - Algebraic Topology

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