Calabi-Yau manifolds are so hot that they may make your LCD monitor or your eyes vibrate.
M. Cicoli, C.P. Burgess, and F. Quevedo have presented their interesting new scenario for string phenomenology:
- extra dimensions accessible at the LHC
- no MSSM superpartners - a non-linear realization of SUSY in the SM sector
- two extra dimensions may be multimicron-sized, much larger than the remaining four
- the remaining four have a K3 shape
- the large 6-volume, and/or the hierarchy between the 2 and 4 extra dimensions, is achieved by some new poly-instanton corrections to the superpotential
Their picture strikingly differs from most scenarios we're used to - where at least some of the superpartners are surely more accessible than extra dimensions.
However, many of the assumptions that are usually made about the models may be just some lore that is subject to intellectual inertia. Many qualitative things could be very different.
The new technical step they use, the poly-instanton corrections, is a method to generate new hierarchies in the size of the extra dimensions. So the whole 6-dimensional volume may be made large - which solves the hierarchy problem.
But the size of the K3 dimensions may be much smaller than the size of the remaining two dimensions of the base: the latter may be of a sub-millimeter size. In that case, they may break the SUSY at a sub-eV scale.
I still haven't understood how they avoid light superpartners if SUSY is broken at this super low, sub-eV scale. At any rate, if this super low SUSY breaking scale makes any sense, it could also be a promising way to solve the cosmological constant problem because the cosmological constant is not far from a quartic millielectronvolt.
Amusingly enough, they tend to predict LHC-accessible Kaluza-Klein modes - signs of extra dimensions - even if all the six dimensions are equally large. That would usually not be the case but in their model, the predicted modes live at some small cycles of their manifold.
Aside from the TeV-scale signs of extra dimensions from the previous paragraph, they also predict lots of light moduli.
Well, I am not able to prove that the model is impossible right now. It may change rather quickly and a bright reader may change it instantly. But I still feel that it is a very bold claim that such a radically different scenario may be made consistent with the known physics and constraints on new physics.