String Phenomenology: Days 4 & 5

Well, my blogging momentum ran out towards the end of last week, but I will wrap up the String Pheno series with some points of note from the last two days.

In a day dominated by F-theory talks (at least in the plenary sessions), I thought the best of the lot was from Eran Palti, who discussed 'ultra-local' model-building in F-theory. The idea is to focus on the neighbourhood of a single point in the compact geometry, where all the important interactions are supported. His main point was that in many string models, we don't actually have enough control to calculate physical coupling constants; often an overall proportionality factor is missing, and simply assumed to be 'of order one' (i.e. of magnitude between about .1 and 10). I think this is a very important point; 'string phenomenology' as it stands is a bit of a misnomer, because as far as I know, nobody has yet been able to do an honest calculation of all quantities like masses and coupling constants in a realistic string model.

Eran offered these ultra-local models as a case where proper calculations can be done, and gave examples where parameters which might have been assumed to be order one actually come out to be much smaller (e.g. $\sim 10^{-8}$).

Luis Ibañez opened the final day with, in my opinion, a somewhat bizarre talk. Roughly speaking, he advocated a scenario in which physics is described by the (fine-tuned) standard model up to about $10^{11}$ GeV, where supersymmetry is broken. The grand unification scale is low, at $\sim 3 \times 10^{14}$ GeV, with the gauge couplings not actually unifying; this, as well as the usual problems of proton decay etc. in 4D GUTs, are supposed to be solved by extra-dimensional effects from F-theory. I think the primary motivation for this setup was twofold:

• In the standard model with a 125 GeV Higgs boson, the Higgs quartic coupling $\lambda$ runs to zero at around $10^{11}$ GeV, and then negative at higher energies, destabilising the vacuum.
• Ibañez claimed (and I think it is probably true) that SUSY is 'generically' broken at quite a high scale in flux compactifications with stabilised moduli.

The link between SUSY breaking and the vanishing Higgs quartic coupling wasn't clear to me; the quartic coupling vanishes in SUSY for $\tan(\beta) = 1$, and I'm not sure how this was being cooked up. The vanishing of $\lambda$ at intermediate scales in the standard model might be an intriguing hint for new physics, but I don't find the possibility of high-scale SUSY breaking very compelling. If the SUSY-breaking scale is high enough, of course, one ends up with an April Fools' Day joke.

There is nothing inconsistent about a theory which has just the standard model spectrum up to high energies (plus something to account for dark matter, but this can be completely decoupled), but accepting this fine-tuning amounts to giving up, in my opinion. If I really believed that there is no dynamical reason for the low electroweak scale, and hence nothing new to be seen at the LHC, then high energy physics would lose most of its interest for me, at least as a field of research.

Altogether, I found this a very enjoyable and stimulating conference. One thing which it has solidified in my mind is that the moduli sector is actually of central importance for string model-building. If the moduli are ignored, then it is not too hard (these days) to find your favourite particle physics model in string theory. If you demand that the moduli are all stabilised in consistent way, then it becomes a much more constrained problem. I have already discussed the arguments of Acharya et al., but see also this paper (which is not so recent, I know) for a discussion of these issues in type IIB theories, and the recent work of Lara Anderson and collaborators on moduli stabilisation in heterotic theories.