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.
