Abstract
Bazhanov-Stroganov (4-simplex) maps are set-theoretical solutions to the 4-simplex equation, namely the fourth member of the family of n-simplex equations, which are fundamental equations of mathematical physics. In this paper, we develop a method for constructing Bazhanov-Stroganov maps as extensions of tetrahedron maps which are set-theoretical solutions to the Zamolodchikov tetrahedron (3-simplex) equation. We employ this method to construct birarional Bazhanov-Stroganov maps which boil down to the famous electric network and Hirota tetrahedron maps at a certain limit.
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Acknowledgments
The work on sections 2, 3 and 4 is funded by the Russian Science Foundation (Grant No. 21-71-30011), https://rscf.ru/en/project/21-71-30011/. The work on sections 1, 5 and 6 was supported by the Ministry of Science and Higher Education of the Russian Federation (Agreement on provision of subsidy from the federal budget No. 075-02-2024-1442). I would like to thank S. Igonin for various useful discussions.
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Konstantinou-Rizos, S. Electric network and Hirota type 4-simplex maps. J. High Energ. Phys. 2024, 94 (2024). https://doi.org/10.1007/JHEP06(2024)094
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DOI: https://doi.org/10.1007/JHEP06(2024)094