Tying knots in particle physics

Lord Kelvin's pioneering hypothesis that the identity of atoms is knots of vortices of the aether had a profound impact on the fields of mathematics and physics despite being subsequently refuted by experiments. While knot-like excitations emerge in various systems of condensed matter physics, the fundamental constituents of matter have been revealed to be elementary particles such as electrons and quarks, seemingly leaving no room for the appearance of knots in particle physics. Here, we show that knots indeed appear as meta-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. Our findings exhibit the significant role of knots in particle physics and represent a modern version of Kelvin's hypothesis.