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High Energy Physics - Theory

arXiv:2205.12238 (hep-th)
[Submitted on 24 May 2022]

Title:Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed

Authors:A. Morozov, N. Tselousov
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Abstract:For a peculiar family of double braid knots there is a remarkable factorization formula for the coefficients of the differential (cyclotomic) expansion (DE), which nowadays is widely used to construct the exclusive Racah matrices $S$ and $\bar S$ in arbitrary representations. The origins of the factorization remain obscure and the special role of double braids remains a mystery. In an attempt to broaden the perspective, we extend the family of double braids to antiparallel triple pretzels, which are obtained by the defect-preserving deformation from the trefoil and all have defect zero. It turns out that factorization of DE coefficients is violated quite strongly, still remains described by an elegant formula, at least for all symmetric representations.
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Geometric Topology (math.GT)
Cite as: arXiv:2205.12238 [hep-th]
  (or arXiv:2205.12238v1 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2205.12238
Related DOI: https://doi.org/10.1140/epjc/s10052-022-10851-7

Submission history

From: Nikita Tselousov [view email]
[v1] Tue, 24 May 2022 17:47:20 UTC (31 KB)
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