Braided matter interactions in quantum gravity via 1-handle attachment

Abstract

In a topological description of elementary matter proposed by Bilson-Thompson, the leptons and quarks of a single generation, together with the electroweak gauge bosons, are represented as elements of the framed braid group of three ribbons. By identifying these braids with emergent topological excitations of ribbon networks, it has been possible to encode this braid model into the framework of quantum geometry provided by loop quantum gravity. In the case of trivalent networks, it has not been possible to generate particle interactions, because the braids correspond to noiseless subsystems, meaning they commute with the evolution algebra generated by the local Pachner moves. In the case of tetravalent networks, interactions are only possible when the model's original simplicity, in which interactions take place via the composition of braids, is sacrificed. We demonstrate that it possible to preserve both the original classification of fermions, as well as their interaction via the braid product, if we embed the braid in a trivalent scheme, and supplement the local Pachner moves, with a non-local and graph changing 1-handle attachment. Moreover, we use Kauffman-Lins recoupling theory to obtain invariants of braided networks that distinguish topological configurations associated to particles in the Bilson-Thompson model.

arXiv comment15 pages, 7 figures. v4: Improvements on exposition. Final version to appear in Phys. Rev. D

References in corpus (14)

• Quantum gravity and the standard model
• A new look at loop quantum gravity
• A topological model of composite preons
• Braids, normed division algebras, and Standard Model symmetries
• Propagation and interaction of chiral states in quantum gravity
• Particle Topology, Braids, and Braided Belts
• On Braid Excitations in Quantum Gravity
• The Standard Model particle content with complete gauge symmetries from the minimal ideals of two Clifford algebras
• C, P, and T of Braid Excitations in Quantum Gravity
• Emergent Braided Matter of Quantum Geometry
• Effective Theory of Braid Excitations of Quantum Geometry in terms of Feynman Diagrams
• A topological model of composite preons from the minimal ideals of two Clifford algebras
• Locality and Translations in Braided Ribbon Networks
• Invariants of Handlebody-Knots via Yokota's Invariants

Cited by in corpus (2)

• Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions
• Contactless generation and trapping of hydrodynamic knots in sessile droplets by acoustic screw dislocations