String-net

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In condensed matter physics, a string-net is an extended object whose collective behavior has been proposed as a physical explanation for topological order by Michael A. Levin and Xiao-Gang Wen. A particular string-net model may involve only closed loops; or networks of oriented, labeled strings obeying branching rules given by some gauge group; or still more general networks.

Their model purports to show the derivation of photons, electrons, and U(1) gauge charge, small (relative to the planck mass) but nonzero masses, and suggestions that the higgs boson, graviton, and quarks and gluons can be modelled in the same way. However, their model does not account for chiral fermions.

For strings labeled by the positive integers, string-nets are the spin networks studied in loop quantum gravity. This has led to the proposal by Levin and Wen^[1] , and Smolin, Markopolou and Tomasz^[2] that loop quantum gravity's spin networks can give rise to the standard model of particle physics through this mechanism, along with fermi statistics and gauge interactions. To date, a rigorous derivation from LQG's spin networks to Levin and Wen's spin lattice has yet to be done, but the project to do so is called "quantum graphity", and in a more recent paper, Tomasz Konopka, Fotini Markopoulou, Simone Severini argued that there are some similarities to spin networks (but not necessarily an exact equivalence) that gives rise to U(1) gauge charge and electrons in the string net mechanism^[3].

Herbertsmithite may be the only known example of String-net matter.^{[4] [5]}

[edit] References

• Levin, Michael A. and Xiao-Gang Wen (January 2005). "String-net condensation: A physical mechanism for topological phases" (abstract). Physical Review B: Condensed Matter and Materials Physics 71 (045110): 21. doi:10.1103/PhysRevB.71.045110. 

1. ^ Title: Photons and electrons as emergent phenomena Michael Levin, Xiao-Gang Wen http://arxiv.org/abs/cond-mat/0407140 page 8 "loop quantum gravity appears to be a string net condensation..."
2. ^ http://arxiv.org/abs/hep-th/0611197 "we argue, but do not prove, that loop quantum gravity's spin networks can reproduce Levin and Wen's string net condensation in quantum graphity page 3
3. ^ Quantum Graphity: a model of emergent locality http://arxiv.org/abs/0801.0861 page #19 "the excitation of the ground state...is expected to give rise to U(1) gauge charge, ...main difference between this model and the original model of Levin and Wen is that in the present case the background is dynamical, and has hexagonal rather than square plaquettes
4. ^ www.EurekAlert.org - Have researchers found a new state of matter?
5. ^ www.newscientist.com - The universe is a string-net liquid