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Tying Knots in Particle Physics

Minoru Eto1,2,3, Yu Hamada4,2, and Muneto Nitta5,2,3

  • 1Department of Physics, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata, Yamagata 990-8560, Japan
  • 2Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan
  • 3International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, 1-3-2 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8511, Japan
  • 4Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
  • 5Department of Physics, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan

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Phys. Rev. Lett. 135, 091603 – Published 29 August, 2025

DOI: https://doi.org/10.1103/s3vd-brsn

Abstract

Knots emerge in various fields of mathematics and physics today. We show that knots indeed appear as stable solitons in a realistic extension of the standard model of particle physics that provides the QCD axion and right-handed neutrinos. This result suggests that, during the early Universe, a “knot dominated era” may have existed, where knots were a dominant component of the Universe, and this scenario can be tested through gravitational wave observations. Furthermore, we propose that the end of this era involves the collapse of the knots via quantum tunneling, leading to the generation of matter-antimatter asymmetry in the Universe.

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Phys. Rev. Lett. 135, 091603– Published 29 August, 2025
  • Received 30 December 2024
  • Revised 4 August 2025
  • Accepted 8 August 2025
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