A few links for your weekend reading:
- If you just can’t get enough of the Multiverse, Inference has commentary on Max Tegmark from Daniel Kleitman and Sheldon Glashow.
- Coverage of the important topic of blackboards is to be found here. To those ill-informed sorts who think that blackboards are the past, whiteboards or some other technology the future, I’ll point out the following. When I came to Columbia back in 1989, there was a recently installed modest-sized whiteboard in the math department common room. Everyone hated it, and after many years it was replaced by a similar-sized blackboard. Last year, in a renovation of the lounge, that blackboard was replaced by a better one, and one whole wall of the room was replaced by a floor-to-ceiling blackboard. A year or so ago, a newly renovated Theory Center was unveiled here in the Physics department: floor-to-ceiling, wall-to-wall blackboards. That’s the future, the whiteboard is the past.
- The latest CERN Courier has a long article by Hermann Nicolai, mostly about quantum gravity. Nicolai makes the following interesting comments about supersymmetry and unification:
To the great disappointment of many, experimental searches at the LHC so far have found no evidence for the superpartners predicted by N = 1 supersymmetry. However, there is no reason to give up on the idea of supersymmetry as such, since the refutation of low-energy supersymmetry would only mean that the most simple-minded way of implementing this idea does not work. Indeed, the initial excitement about supersymmetry in the 1970s had nothing to do with the hierarchy problem, but rather because it offered a way to circumvent the so-called Coleman–Mandula no-go theorem – a beautiful possibility that is precisely not realised by the models currently being tested at the LHC.
In fact, the reduplication of internal quantum numbers predicted by N = 1 supersymmetry is avoided in theories with extended (N > 1) supersymmetry. Among all supersymmetric theories, maximal N = 8 supergravity stands out as the most symmetric. Its status with regard to perturbative finiteness is still unclear, although recent work has revealed amazing and unexpected cancellations. However, there is one very strange agreement between this theory and observation, first emphasised by Gell-Mann: the number of spin-1/2 fermions remaining after complete breaking of supersymmetry is 48 = 3 × 16, equal to the number of quarks and leptons (including right-handed neutrinos) in three generations (see “The many lives of supergravity”). To go beyond the partial matching of quantum numbers achieved so far will, however, require some completely new insights, especially concerning the emergence of chiral gauge interactions.
I think this is an interesting perspective on the main problem with supersymmetry, which I’d summarize as follows. In N=1 SUSY you can get a chiral theory like the SM, but if you get the SM this way, you predict for every SM particle a new particle with the exact same charges (behavior under internal symmetry transformation), but spin differing by 1/2. This is in radical disagreement with experiment. What you’d really like is to use SUSY to say something about internal symmetry, and this is what you can do in principle with higher values of N. The problem is that you don’t really know how to get a chiral theory this way. That may be a much more fruitful problem to focus on than the supposed hierarchy problem.
- Progress in geometric Langlands marches on, with a new paper yesterday from Aganagic, Frenkel and Okounkov on the Quantum q-Langlands Correspondence, a two-parameter generalization of geometric Langlands. Among many other things, they formulate (Conjecture 6.3) a conjecture generalizing the characterization (using BRST methods) of affine Lie algebra representations at the critical level that from the beginning of the subject described a major aspect of how geometric Langlands works locally (for details on this, see Frenkel’s book Langlands Correspndence for Loop Groups).