Categorifying the Knizhnik-Zamolodchikov Connection
Abstract
In the context of higher gauge theory, we construct a flat and fake flat 2-connection, in the configuration space of particles in the complex plane, categorifying the Knizhnik-Zamolodchikov connection. To this end, we define the differential crossed module of horizontal 2-chord diagrams, categorifying the Lie algebra of horizontal chord diagrams in a set of parallel copies of the interval. This therefore yields a categorification of the 4-term relation. We carefully discuss the representation theory of differential crossed modules in chain-complexes of vector spaces, which makes it possible to formulate the notion of an infinitesimal 2-R matrix in a differential crossed module.
Keywords
Cite
@article{arxiv.1106.0042,
title = {Categorifying the Knizhnik-Zamolodchikov Connection},
author = {Lucio S. Cirio and João Faria Martins},
journal= {arXiv preprint arXiv:1106.0042},
year = {2017}
}
Comments
30 pages, 2 figures; v3: final version to be published in Differential Geometry and its Applications