A friend today showed me this post and after reading Prof. Wen's answer, few questions came to my mind. Prof. Wen says:

all fermions (elementary or composite) must carry gauge charges (see cond-mat/0302460). The standard model contain composite fermions that are neutral for $U(1)×SU(2)×SU(3)$ gauge theory. So according to the string-net theory, the standard model is incomplete. The correct model should contain extra gauge theory, such as a Z2 gauge theory.

But, As far as I know (and understand), Coleman-Mandula theorem states, more or less, that space time symmetries (which determine spin) cannot mix with gauge symmetries in anyway. Haag-Lopuszanski-Sohnius extension of this theorem states that the only possible loophole to the Coleman-Mandula theorem is SUSY. So, is the Standard Model incomplete from the point of view of string-net theory or is string-net theory radically inconsistent (with what we see in nature), and could therefore be wrong in its present form? Also, is it meaningful to call something a $Z_2$ gauge theory? Because, as far as I understand, discrete symmetries can at best act as large gauge transformations.

PS: Prior to today, I had no idea about string-net theory and I definitely haven't studied it, formally.

  • $\begingroup$ I think that this question hasn't been replied to because the source of many statements is fuzzy and it's all confusing. Why shouldn't composite fermions ever be singlets? The neutron is basically a singlet, especially if the baryon number is ultimately not conserved. A theory that prevents one from creating arbitrary bound states almost certainly disagrees with the observations - and with locality. So why should one spend too much time with the question what the theory actually is? If it makes these strange prdictions, it's probably not too interesting. $\endgroup$ – Luboš Motl Apr 4 '16 at 14:17

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