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Paul Frampton: three generations from an extension of SM

Paul Frampton, an achieved physicist, former TRF guest blogger, a sex symbol among the Argentine supermodels, and an involuntary importer of a substance is impressing everyone with the physics productivity during his confinement in Argentina where he is affiliated with Centro Universitario DeVoto in Buenos Aires.

Five days ago, a North Carolina judge endorsed the decision of University at Chapel Hill not to pay Paul his salary. Most people at UNC believe he is innocent.

Valeria Mazza, a Ms Frampton candidate

They just published the first part of his Notes From the Gallows:

Three Generations in Minimally Extended Standard Models (arXiv)
Paul's co-authors are Chiu Man Ho and Thomas W. Kephart. And I actually think it's a very interesting preprint.

In the Standard Model gauge group, \(SU(3)_C\times SU(2)_L\times U(1)_Y\), they replace \(SU(2)_L\) by \(SU(N)_L\) with a higher value of \(N\). So the electroweak doublets are replaced by larger multiplets and there are new particles whose electric charges differ from those of the known leptons and quarks by integer multiples of the electron's charge. Also, the hypercharge \(Y\) is replaced by a more general generator \(X\) which acquires corrections, \(Y=X+\dots\), whenever \(N\geq 2\).

That could be boring except that the authors show something interesting about the extended Standard Model. They are actually able to cancel all triangle anomalies. Note that the spectrum is more complicated than it is in the Standard Model and even the cancellation in the Standard Model looks nontrivial. However, the cancellation in the Standard Model is easily proved by an embedding into a grand unified theory, something that isn't quite available here.

So the cancellation in their extended Standard Model is even more nontrivial but they're able to achieve it. They can find infinitely many models that cancel all gauge anomalies but they have one surprising – and nicely surprising – feature: all of these new models require three generations. In their theory, they must make the first two generations analogous when it comes to their quantum numbers but the third generation has to be different. When these building blocks are combined, the anomaly cancellation conditions hold. All of them do.

The value \(N=5\), the maximum value compatible with the QCD's asymptotic freedom that Paul keeps on believing in despite his confinement, is given a special treatment.

If you're returning from Argentina through San Francisco, you need some flowers instead of cocaine and some gentle people around you.

Of course, there's probably no simple counterpart of the \(SO(10)\) grand unification here: one would need a larger orthogonal group whose spinor would be much bigger than needed. I don't know whether the enhanced Standard Model could fit into some natural \(SU(5)\)-like grand unification. Needless to say, the models above assume that there is no SUSY: with the superpartners included, the asymptotic freedom would probably disappear for smaller values than \(N=5\).

Given the circumstantial data based primarily on the stringy vacua, I don't believe that these strange gauge groups and representations may realistically describe the hypothetical beyond-the-Standard-Model physics but the cancellation they're able to achieve still looks interesting although I would have to play with this model and many others to decide how nontrivial the cancellation actually is. One should appreciate that the more charges and dimensions-of-representations of the new matter fields you may adjust, the less constraining the anomaly conditions (for a pretty much fixed amount of cubic combinations of the generators) should become. So it may have been a priori guaranteed that one may find 3-generation models that cancel the anomalies for an extended Standard Model group if the generations are allowed to be different.

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snail feedback (1) :

reader MW said...

Dear Lubos,

It could be helpful to Paul if you would publish this message in a prominent place on The Reference Frame.

Three days ago in a phone call from the prison Paul told me that sometime before the end of May, there is supposed to be a judgment that should give one of the following three outcomes:

-he would be allowed to leave Argentina

-he would be freed from the prison but without his passport, and required to stay in Argentina until his trial

-he would have to remain in prison until his trial.

He said that the standard prison term for carrying the amount of cocaine (2kg) that was found in the bag he was given is about four and a half years.

Paul said it could have a positive influence on the upcoming hearing if as many colleagues as possible would send character references. He recommended that such a letter include a statement about how long and in what capacity you have known him, and a statement that you have never known him to use any kind of illegal drugs.

He has new lawyers now. They are Laura Vouilloud and Vanina Bessante. Letters may be sent to them at


I suggest putting ``character reference for Paul Frampton" in the subject heading. To have an impact the letter should be sent as soon as possible. This is one of the few opportunities the physics community may have to do something that might help Paul avoid a long prison term.

As far as I could tell, Paul sounded like his old self on the phone the other day. However, he did have a cough.

Thanks for your help,

Mark Williams
Professor of Mathematics
UNC Chapel Hill