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TMF, 2017, Volume 192, Number 1, Pages 115–163 (Mi tmf9214)  

This article is cited in 1 scientific paper (total in 1 paper)

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

Abstract: 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.

Keywords: Chern–Simons theory, knot theory, virtual knot, matrix model.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
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).


DOI: https://doi.org/10.4213/tmf9214

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English version:
Theoretical and Mathematical Physics, 2017, 192:1, 1039–1079

Bibliographic databases:

Document Type: Article
Received: 23.04.2016

Citation: 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
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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