Pith. sign in

REVIEW 1 cited by

Categorifying the Knizhnik-Zamolodchikov Connection

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1106.0042 v3 pith:F3WCFR5N submitted 2011-05-31 hep-th math.CTmath.QA

classification hep-thmath.CTmath.QA
keywords categorifyingconnectioncrosseddifferentialchorddiagramsflathorizontal
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

In the context of higher gauge theory, we construct a flat and fake flat 2-connection, in the configuration space of $n$ 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 $n$ 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings

    math.QA 2025-05 conditional novelty 7.0 of 10

    A coherent totally symmetric strict infinitesimal 2-braiding gives a second-order deformation quantization to a braided monoidal cochain 2-category, and 3-shifted Poisson structures induce syllepses.

Pith tools