I was down in Princeton today and went to hear Witten’s physics department colloquium on the topic of “Supersymmetry: Pro or Con”. He spent most of the hour going over the 25 year-old hierarchy argument for supersymmetry (that supersymmetry provides a reason for the Higgs to be much lighter than the Planck scale, since it is paired with a fermion whose mass can be protected by an approximate chiral symmetry).
He gave the following arguments for believing in GUTs:
1. Can naturally get small neutrino masses via the see-saw mechanism.
2. Coupling constant unification to 1%
3. Tentative evidence from CMB that fluctuations come from GUT scale.
Actually none of these seem to me very convincing (and to claim 1% coupling constant unification I think he has to use 1-loop results, at 2-loops it is more like 5-10% off, but this may depend on exactly what you are comparing to what).
His points in favor of supersymmetry were:
1. Solves hierarchy problem.
2. Coupling constant unification again.
3. Prediction of top mass from supersymmetric SO(10) GUT.
4. Supersymmetry is consistent with all accelerator data.
5. Lowest mass superpartner a good candidate for dark matter.
6. Part of string theory.
Again none of these are really convincing. If you don’t believe in GUTs, the GUT scale is irrelevant, and since we don’t understand quantum gravity, the significance of the Planck scale is also unclear. I’m no expert on supersymmetric GUT “predictions”, but they seem to depend on lots of choices for the details of the GUT, how its symmetry breaks, and how fermions get masses from the symmetry breaking. Saying that supersymmetry is consistent with all accelerator data is kind of strange since the standard model without supersymmetry is consistent with all accelerator data and there is no evidence for supersymmetry. You can guess what I think of his last argument.
His points against supersymmetry were:
1. The Higgs mass bound is already embarassingly high, need some fine-tuning to get a Higgs that massive in a supersymmetric theory.
2. Supersymmetry spoils many of the experimental successes of the standard model since it generically has experimentally disallowed amounts of violation of CP, baryon and lepton number conservation, flavor-changing neutral currents.
3. No good picture of how to break supersymmetry.
Well, for me the con has it over the pro, but Witten still seems to hold out hope that supersymmetry will be found at the LHC. At the end of his talk, he discussed what he called the “worst case scenario”; that LHC sees a Higgs particle, but nothing else: no supersymmetry, no technicolor, no Little Higgs, no extra dimensions. He said that if this happens people will look for anthropic explanations of the hierarchy problem, whereas if the LHC found something that explained the hierarchy problem, they might be encouraged to look again for non-anthropic answers to the cosmological constant problem (which he claimed was analogous to the hierarchy problem). He did say “I hope it is wrong” about the anthropic explanation of the cosmological constant.
On the anthropic front, Michael Dine is claiming that maybe the statistical analysis of the landscape will “predict” that supersymmetry breaking is at a low energy scale. The arguments he gives sound to me like a complete joke, and from what I remember Michael Douglas was recently claiming that the same kind of analysis indicated that supersymmetry was broken at a high energy scale. One other funny thing about Dine: he doesn’t say that the landscape makes predictions, but that it is “the first predictive framework we have encountered”. This is a guy who for nearly twenty years has been giving talks on “superstring phenomenology” and claiming that any day now string theory would make predictions. I wonder why in all of those previous talks he neglected to mention that not only were there no predictions from string theory, there wasn’t even a “predictive framework”.
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