Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 014, 43 pages      arXiv:1109.0080
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Emergent Braided Matter of Quantum Geometry

Sundance Bilson-Thompson a, Jonathan Hackett b, Louis Kauffman c and Yidun Wan d
a) School of Chemistry and Physics, University of Adelaide, SA 5005, Australia
b) Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada
c) Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045, USA
d) Open Research Centre for Quantum Computing, Kinki University, Kowakae 3-4-1, Higashi-osaka 577-0852, Japan

Received August 31, 2011, in final form March 12, 2012; Published online March 24, 2012

We review and present a few new results of the program of emergent matter as braid excitations of quantum geometry that is represented by braided ribbon networks. These networks are a generalisation of the spin networks proposed by Penrose and those in models of background independent quantum gravity theories, such as Loop Quantum Gravity and Spin Foam models. This program has been developed in two parallel but complimentary schemes, namely the trivalent and tetravalent schemes. The former studies the braids on trivalent braided ribbon networks, while the latter investigates the braids on tetravalent braided ribbon networks. Both schemes have been fruitful. The trivalent scheme has been quite successful at establishing a correspondence between braids and Standard Model particles, whereas the tetravalent scheme has naturally substantiated a rich, dynamical theory of interactions and propagation of braids, which is ruled by topological conservation laws. Some recent advances in the program indicate that the two schemes may converge to yield a fundamental theory of matter in quantum spacetime.

Key words: quantum gravity; loop quantum gravity; spin network; braided ribbon network; emergent matter; braid; standard model; particle physics; unification; braided tensor category; topological quantum computation.

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