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In Xiao-Gang Wen's review of topological order http://arxiv.org/abs/1210.1281 , he states in footnote 52 that string-nets are so far unable to produce the chiral coupling between the SU(2) gauge boson and the fermions. Is it known how this chiral coupling can be expressed in lattice gauge theory, and the remaining question is one of emergence; or is it the case that its expression in lattice gauge theory is unknown, analogous to the chiral fermion question which took many years to solve?

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My impression is that we have the same problem in lattice gauge theory, which is so far unable to produce the chiral coupling between the SU(2) gauge boson and the fermions. I understand that there is some progress, but I do not know if the problem is fully solved. –  Xiao-Gang Wen Jan 5 '13 at 22:09
    
Thanks for the reply! As you say, it does seem not fully solved yet. Kaplan's review arxiv.org/abs/0912.2560 says "there is currently no practical way to regulate general nonabelian chiral gauge theories on the lattice." Poppitz and Shang arxiv.org/abs/1003.5896 say "we do not yet have a method of approximating an arbitrary chiral gauge theory by latticizing and then simulating it on a computer|even in principle." –  Andrew Tan Jan 6 '13 at 3:51

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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 fermions.

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