Black magic session of concordance: Regge mass spectrum from Casson’s invariant

Abstract

Recently, there had been a great deal of interest in obtaining and describing all kinds of knots in links in hydrodynamics, electrodynamics, non-Abelian gauge field theories and gravity. Although knots and links are observables of the Chern–Simons (CS) functional, the dynamical conditions for their generation lie outside the scope of the CS theory. The nontriviality of dynamical generation of knotted structures is caused by the fact that the complements of all knots/links, say, in S3are 3-manifolds which have positive, negative or zero curvature. The ability to curve the ambient space is thus far attributed to masses. The mass theorem of general relativity requires the ambient 3-manifolds to be of nonnegative curvature. Recently, we established that, in the absence of boundaries, complements of dynamically generated knots/links are represented by 3-manifolds of nonnegative curvature. This fact opens the possibility to discuss masses in terms of dynamically generated knotted/linked structures. The key tool is the notion of knot/link concordance. The concept of concordance is a specialization of the concept of cobordism to knots and links. The logic of implementation of the concordance concept to physical masses results in new interpretation of Casson’s surgery formula in terms of the Regge trajectories. The latest thoroughly examined Chew–Frautschi (CF) plots associated with these trajectories demonstrate that the hadron mass spectrum for both mesons and baryons is nicely described by the data on the corresponding CF plots. The physics behind Casson’s surgery formula is similar but not identical to that described purely phenomenologically by Keith Moffatt in 1990. The developed topological treatment is fully consistent with available rigorous mathematical and experimentally observed results related to physics of hadrons.