All too soon, my visit to Perimeter came to an end yesterday, and I'm now writing from the University of Pennsylvania, in Philadelphia. I'm here all this week on the kind invitation of Ron Donagi, and I'll be giving a seminar tomorrow, which will be very similar to the one I gave at PI. This is my second visit to U.Penn., the first being last year for the fantastic String Math conference.
Let me mention one interesting aspect of the last week. I had the chance to talk at some length with John Dixon (I recommend reading his short profile; he has had a very unconventional career), and in particular he explained a little bit about an idea he has been working on for several years, which he calls 'CyberSUSY'. You can find the papers on the arXiv. It's a rather complicated idea, which I couldn't possibly explain fully here even if I understood it, but I can outline some of the ingredients.
The theory includes a non-standard realisation of supersymmetry, and an infinite tower of arbitrarily high-spin fields, carrying the quantum numbers of the standard model fields (this sounds bizarre, but is reminiscent of the tower of massive modes one finds in string theory). The supersymmetry-invariance of the action depends on the invariance of the superpotential under certain transformations, which are not usually considered because they do not leave the kinetic terms invariant (and therefore are not symmetries of the theory). John's point of view is that this ties supersymmetry together with the gauge symmetry and multiplet structure of the standard model. Furthermore, upon the addition of a dimensionful parameter, electroweak symmetry and supersymmetry are both broken.
I have some misgivings about this scenario:
- It seems to me that, although electroweak symmetry is indeed spontaneously broken, supersymmetry is broken explicitly, because the additional term spoils the invariance of the superpotential under the special transformations which John relies on. Perhaps such a term could be generated spontaneously in some enlarged supersymmetric theory, but this isn't clear.
- I think the same tricks might work, for example, in a minimal $SU(5)$ GUT model, which would lead to $SU(4)$ as the low energy gauge symmetry of the universe. If this is true (I think John is going to check), the link with the gauge structure of the standard model is broken, and this is one of the arguments for the set up.
- The theory must ultimately be coupled to (super)gravity. The distinction between the superpotential and the Kähler potential then becomes muddied, and the strange requirement of invariance of the superpotential, but not the kinetic terms, might not generalise in any meaningful way to a supergravity extension.