Tuesday, April 28, 2009

F-theory bottom-up uprising: CP3 blowups



The F-theory phenomenological minirevolution is going on. Joseph Marsano, Natalia Saulina, and Sakura Schafer-Nameki (Caltech) wrote a 55-page paper called
F-theory compactifications for supersymmetric GUTs (PDF)
that constructs very explicit Calabi-Yau four-folds that produce SU(5) grand unified theories if used as backgrounds for F-theory.

As the final picture for the base manifold, including the diamond E' in the middle, indicates, they obtain the space by a sequence of blowups and flops, starting from CP3. Recall that CP3 is a toric geometry with a simplex as its toric diagram: you find it in the paper, too. Many of the world's best geometers below 40 were helping them to understand the manifolds.

In my opinion, the complex projective space is the most natural starting point for local constructions because among complex geometries, it is the simplest compact approximation of the flat space. However, a couple of operations have to be performed for the consistency conditions to be obeyed.




They find out that the conditions for viable phenomenological features - such as three generations with hierarchical masses, the unbroken U(1) hypercharge, and the main principle behind the botttom-up phenomenology (decoupling of Planck and GUT physics) - arise naturally in these constructions. They're the first professionals who write a full-quality paper that takes Donagi-Wijnholt as well as Beasley-Heckman-Vafa papers into account.

Donagi and Wijnholt actually performed a more complete local & global analysis than Vafa et al. - which might be used as a simple description of the apparent limited degree of interactions between those two teams and the marginal contradictions between their papers - and Marsano et al. may be going even further in the accuracy of their analysis. These backgrounds really exist, they're nice, and they're simple.

Heterotic strings used to be the most natural and likely realizations of the real world within string theory. Many of the F-theory constructions in these minirevolutionary papers have heterotic duals but the most phenomenologically promising F-theoretical bottom-up vacua actually don't admit conventional heterotic duals at all.

Concerning the diversity discussions, this perfectionist paper has quite a diverse collection of authors. One author is a woman (privet, NS!). Another author belongs to an even more special group: she is a woman of color. But that's nothing compared to the third author who is a conservative in the Academia (hi, Joe!). ;-)

Some other papers

By the way, Asia is getting mad about the Hořava-Lifshitz Lorentz-breaking UV-complete general relativity. Today, there are three hep-th papers about this topic. Sorry but I won't declare the situation another minirevolution because at least so far, I view this framework as unmotivated.

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