I have a doubt regarding String-Net theory. Prof. Xiao-Gang Wen stresses upon the point that all fermions must carry gauge charges. The Standard Model contain composite fermions that are neutral for U(1) × SU(2) × SU(3) gauge theory. So, according to string-net theory the Standard Model of particle physics is incomplete, and the correct/complete model should contain extra gauge theory, such as a Z_2 gauge theory. But, Coleman-Mandula theorem states, more or less, that space time symmetries (which determine spin) cannot mix with gauge symmetries in anyway. The Haag-Lopuszanski-Sohnius (HLS) extension of this theorem states that the only possible loophole to the Coleman-Mandula theorem is SUSY, as far as I understood. 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 must 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: To get an understanding/gist of what Prof. Wen is saying (as I mentioned in the first half of my question) please refer to this paper: http://arxiv.org/abs/cond-mat/0302460
Dear Nihan,
I'm not an expert in this field but I think that the incompleteness of th SM theory could be found in the theory itself and/or in comparison with experimental evidences.
I'll explain myself:
- the SM is based on about 15-20 unmeasurable parameteres, this is not a good quality for a would-be complete theory. Moreover, it has an extraordinary ability to predict a huge amount of phenomena and it is able to unify three of the four fundamental interactions. The problem is the inability to explain gravitational effects in the same framework.
- some experimental evidences already have underlined several limits of this theory (think about massive neutrinos, first dark matter detections, and so on)
I think that the incompleteness of SM is a well-defined question in quantum comunity, but at the same time it remains the "best fitting theory" of the reality as we know it today.
New theories need (based or not on the SM theory itself) but the incompleteness of a theory is defined by experiments and observation of nature: these are the only true judges of a theory.
@Manuel: Dear Sir, your statement is really strong...In my opinion, the discovery of Higgs' Boson is a statistical prove (five-sigma rule) of how the SM is a wonderful theory although incomplete and a powerful tool to understand how (and not why) things work.
@ Manuel: I'll read your paper again...but I'd like underline that MS theory (as any other one) only describes how things work: "why" things work is the focus of religions and phylosophies in my opinion. MS is a good description of a lot of experimental evidences but it is not a "theory of all", therefore it is incomplete.
On the other hand, I have underlined your statement because is strong...if true, I'm be very happy that a "new shiny light" hits our knowledge of nature, but this is not the focus of discussion. Let me doubt...this is in my nature.
I completely agree with Charles.
Sorry...MS was SM (Standard Model). I appreciate your speculative arguments...but I'm not convinced by your conclusions about the hidden variables. I'll muse on them.
One point is quite clear: the Standard Model is not complete. However it is a useful theoretical framework and a fruitful tool to describe a part of nature. It needs to be overcome, as all theories when they fail. Experiments are the judges.
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