Categorifying the Knizhnik-Zamolodchikov Connection

Details Categorifying the Knizhnik-Zamolodchikov Connection Categorifying the Knizhnik-Zamolodchikov Connection

2011-05-31

arxiv.org/abs/1106.0042v2

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 2 figures; v2: minor corrections, improvement in the presentation

Scientific paper

In the context of higher gauge theory, we categorify the Knizhnik-Zamolodchikov connection in the configuration space of n particles in the complex plane by means of a differential crossed module of (totally symmetric) horizontal 2-chord diagrams, categorifying the 4-term relation. We carefully discuss the representation theory of differential crossed modules in chain-complexes of vector spaces, inside which we formulate the notion of infinitesimal 2-R matrix.

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