Just a short memo.
We have seem that the sBoostrap, which is really a way to produce Chan-Paton labels, drives naturally to SU(15) and then perhaps to SO(30). Which was very encouraging because we know an open string needs to have a SO(32) group asociated to it. Sometimes this group is justifyed as 2^5, with 5 being half of the dimension of space, and it is related to a SO(8192) for bosonic strings.
Our justification to choose the charges, on the other hand, is that they correspond to light quarks. This should be, that there is some way to give mass to the particles in a SO(32) and only the light quarks survive, available to be used as Chan-Paton labels, and then it is Chan-Paton all the way down.
But the real justification for SO(32) is to have an anomaly-free theory. So the question is if our recursivity could be related to anomaly-matching conditions in the way of ‘t Hooft.
There is still the question of why or how some particles get mass, some others travel free. We have not problems with the leptons, they could also be massless but unable to bind into the string due to the lack of colour. Even some coloured objects could we unable to bind if they have not both chiralities available. Well, the point here is that if we consider light quarks plus leptons we are into 84 degrees of freedom and then again in the world of 11D sugra representations.
Comment #7 of fzero
https://www.physicsforums.com/threads/so-32-heterotic-string-theory.829219/
suggests that the reasoning which leads to SO(32) open string in ten dimensions (as a way to cancel gauge and gravity anomalies), can be repeated for specific compactifications.
Meanwhile, I always thought leptons and the electroweak sector might emerge in the IR, via a Seiberg duality with a UV theory which is just quark and gluon superfields. The emergent composite fields in the IR of a Seiberg duality must obey some kind of anomaly matching.
Actually, I’m reminded of a “Hanany-Witten transition”, in which new branes emerge at a brane intersection, which has been a string model of some Seiberg dualities. It would be interesting if emergence of an electroweak sector could be understood that way.