The mirror pair gives a representation of $B_2$ in $B_3$, since it has an obvious inverse and thus generates the integers $Z$. For $B_2$, the number $0$ is the photon braid. Note also that the neutrino braids perform supersymmetry with triality, which underlies the mass quantum numbers.
14 years ago
There is a recent paper which associates braids with quantum field theories with N=2 supersymmetry. (They are only three-dimensional, but they arise from a domain wall in a four-dimensional field theory, and the braids appear to describe spatial variations in the d=4 particle spectrum as you cross the domain wall. The d=3 theory describes particles trapped in the wall.)
ReplyDeleteSo I have been thinking about an N=2 version of the Bilson-Thompson correspondence. In N=2 supersymmetry as normally understood, particles have N=1 superpartners, and then they both have mirror partners which form a second N=1 superfield (in the complex conjugate representation of the gauge group, relative to the first N=1 superfield).
It has occurred to me that you have your "Fourier supersymmetry", and you also have mirrors for the neutrinos. So does this mean you have what amounts to an N=2 structure in the neutrino sector? There is actually an N=1/N=2 hybrid model in the phenomenology literature, but the idea there seems to be that everything is fundamentally N=2, but only the gauge bosons have detectable mirror partners (scalar bosonic super-mirror-partners). I'm going to have to think about an N=2 model where N=2 survives in the neutrino sector, and has something to do with tachyonic dark energy...
OK, Mitchell, I can see you are making progress, but remember that my blog is not the place to record it. Thanks for this link, but if you persist in posting so many links I will start deleting your comments. (You don't have any more rights than all the people who are already banned from this blog).
ReplyDeleteNow, you still don't get that I am not interested in turning braids into Stringy Non Physics. Of course there is a connection between the different supersymmetries, but there is no reason to turn the correct version into an effective stringy version. That will only take you further away from the phenomenology. On the other hand, if you want to spend time convincing a few string theorists about all this, then what you are doing is a good idea, I think.
Sorry if that last comment was curt, but unlike most people, I like efficiency and not verbosity.
ReplyDeleteThese braids would be $N=2$ if, for instance, strands could be Real. Your 'usual' susy is dictated by the number fields, but we never only have Real numbers, since we have Octonions with triality.
No offense taken; I actually admire your ability to retain focus.
ReplyDelete