Braided matter interactions in quantum gravity via 1-handle attachment

TL;DR

This paper introduces a novel method to model particle interactions in quantum gravity by embedding braids in a trivalent network and adding non-local 1-handle attachments, preserving particle classification and enabling interactions.

Contribution

It demonstrates that combining braid embeddings with 1-handle attachments in trivalent networks allows for particle interactions while maintaining fermion classification.

Findings

Preserves fermion classification in braid models.

Enables particle interactions via 1-handle attachments.

Uses recoupling theory to distinguish topological configurations.

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.