This article is cited in 2 scientific papers (total in 2 papers)
Matrix model and dimensions at hypercube vertices
A. Yu. Morozovabc, A. A. Morozovabcd, A. V. Popolitovabe
a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
c National Engineering Physics Institute "MEPhI", Moscow, Russia
d Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk, Russia
e Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands
We consider correlation functions in the Chern–Simons theory (knot polynomials) using an approach in which each knot diagram is associated with a hypercube. The number of cycles into which the link diagram is decomposed under different resolutions plays a central role. Certain functions of these numbers are further interpreted as dimensions of graded spaces associated with hypercube vertices, but finding these functions is a somewhat nontrivial problem. It was previously suggested to solve this problem using the matrix model technique by analogy with topological recursion. We develop this idea and provide a wide collection of nontrivial examples related to both ordinary and virtual knots and links. The most powerful version of the formalism freely connects ordinary knots/links with virtual ones. Moreover, it allows going beyond the limits of the knot-related set of $(2,2)$-valent graphs.
Chern–Simons theory, knot theory, virtual knot, matrix model.
|Russian Science Foundation
|This research was performed at the Institute for
Information Transmission Problems and supported by a grant from the Russian
Science Foundation (Project No. 14-50-00150).
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Theoretical and Mathematical Physics, 2017, 192:1, 1039–1079
A. Yu. Morozov, A. A. Morozov, A. V. Popolitov, “Matrix model and dimensions at hypercube vertices”, TMF, 192:1 (2017), 115–163; Theoret. and Math. Phys., 192:1 (2017), 1039–1079
Citation in format AMSBIB
\by A.~Yu.~Morozov, A.~A.~Morozov, A.~V.~Popolitov
\paper Matrix model and dimensions at hypercube vertices
\jour Theoret. and Math. Phys.
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Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646
A. S. Anokhina, “Knot polynomials from gt-matrices: where is physics?”, Phys. Part. Nuclei, 51:2 (2020), 172–219
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