Higher holonomies: Comparing two constructions |
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Institution: | 1. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany;2. Centre for Quantum Geometry of Moduli Spaces, Ny Munkegade 118, DK-8000 Aarhus C, Denmark |
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Abstract: | We compare two different constructions of higher-dimensional parallel transport. On the one hand, there is the two-dimensional parallel transport associated with 2-connections on 2-bundles studied by Baez–Schreiber 2], Faria Martins–Picken 11] and Schreiber–Waldorf 12]. On the other hand, there are the higher holonomies associated with flat superconnections as studied by Igusa 7], Block–Smith 3] and Arias Abad–Schätz 1]. We first explain how by truncating the latter construction one obtains examples of the former. Then we prove that the two-dimensional holonomies provided by the two approaches coincide. |
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