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I am going to try and reinterpret some of that paper, see if we can get some kind of answer started. Please comment and contribute, I think this is an interesting physical system. It would seem that they are using the fact that there are both boson (symmetric) and fermion (antisymmetric) representations of $SU(N)$ to generalize the usual $SU(2)$ magnet. The ...

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The chiral-fermion/chiral-gauge-theory problem is solved: any anomaly-free chiral gauge theories can be put on lattice by simply turning on a proper interaction. See my new papers http://arxiv.org/abs/1305.1045 and http://arxiv.org/abs/1303.1803 As a result, the string-net theory can also produce the coupling between the SU(2) gauge boson and the chiral ...

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I was wondering about exactly the same question some days ago, reading the seminal paper of Mermin (Rev. Mod. Phys. 51, 591--648 (1979), The topological theory of defects in ordered media), where you find an introductory discussion for the example of spins within the two-dimensional plane. There you find a lot of plots with spins (depicted as arrows in the ...

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