Thursday, June 30, 2011

Realistic physics from D-branes on del Pezzo 3

Today, despite the significant competition, the best TRF-awarded hep-th paper was:
Towards a Systematic Construction of Realistic D-brane Models on a del Pezzo Singularity
by Dolan, Krippendorf, and Quevedo. They construct realistic models on D7- and especially D7-branes on manifolds with del Pezzo singularities.

Del Pezzo surfaces are "somewhat positively curved" cousins of the K3 surface - their real dimension is four - and I began to like them because of the "mysterious duality" which remains a great method to remember many properties of the surfaces. But of course they're important in higher-dimensional geometry for many other reasons and realistic model building could ultimately be more important than the mysterious duality. Or at least equally.

The funny thing that the oldest models of this kind were using C^3/Z_3 which has a dP0 or CP^2 in it. The toric diagram of it is a triangle. This leads to excessively simple, unrealistic models. On the other hand, it's good to have simple enough models. When the del Pezzo surface is eliptically fibered, one obtains a classically massless lightest generation of fermions which is great for realism.

So you may go up to dP4 but the authors actually argue that dP3 is enough to get realistic models with the right supersymmetric Standard Model spectrum, with two Higgs doublets per generation, with realistic fermion masses, stable proton, neutrino masses, and so on. The Standard Model group arises from the breaking of a Pati-Salam group, SU(4) x SU(2) x SU(2).

It's kind of incredible how many realistic features a model that can be pretty much inspired if not defined by the three characters, dP3, produces. It is comparably amazing to the similar ability of the heterotic models. I still believe that people should try to understand the duals of such models in some more detail - and look in the middle of the ocean between the type IIB and heterotic descriptions.

Heterotic duals normally appear only if the type II/M model is defined on a K3 fibration. But I am convinced that there exist modified heterotic descriptions for del Pezzo surfaces, too. A non-trivial dilaton (and/or axion) is probably necessary to match the features by which del Pezzo surfaces differ from a K3. Recall that dP9, the first marginally noncompact del Pezzo surface, may be visualized as one half of a K3.

I usually hate "third ways" but in the case of phenomenology where one has various symmetry breaking schemes etc., I still believe that the truth is "somewhere in between". The real world could sit somewhere at the center of a piece of the landscape that can be approached from different directions - some of them are heterotic, some of them are type IIB or F-theory, and all of them have different breaking schemes for the gauge group.

In field theory, one can't interpolate between the "qualitatively different" kinds of models. But in string theory, you almost certainly can.

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