Thursday, December 03, 2009

U(1)_{PQ} non-GUT exotics restore unification in F-theory

In the first hep-th paper today, Joe Marsano, Natalia Saulina, and Sakura Schafer-Nameki study the detailed impact of the Peccei-Quinn U(1) symmetry in the realistic bottom-up F-theoretical models of string phenomenology.

In a previous paper, they appreciated that a new U(1)_{PQ} symmetry is almost necessary to ban the dimension-four proton decay: the new U(1) charges prohibit a tree-level mu-term. However, with such a new symmetry, one also obtains some non-GUT "incomplete" multiplets that may spoil the gauge coupling unification if the low-energy spectrum contains MSSM fields only.

However, there has been another problem that some of us have kind of missed. Even without such U(1)_{PQ}, the gauge coupling unification is distorted in the F-theory models because of an extra term, "int C_0 tr(F^4)", integrated over the GUT 7-brane.

So there are actually two similar problems that destroy the gauge coupling unification. Now, you may be able to guess how the gospel is going to continue. ;-) The authors make detailed calculations of the impact on the unification and find out that the two distortions of the unification exactly cancel!

Building on their April 2009 geometry, they find a handful of three-generation models, including some of those where anti-D3-branes are not needed to cancel the tadpole (and such models are arguably prettier and more likely to be stable and healthy). The new non-GUT matter may be good not only for preventing unwanted interactions but also for communication of SUSY breaking although the latter statement may contain some wishful thinking because the detailed mechanism of these would-be messenger fields has not yet been analyzed.

Some SU(5) singlets may be good as right-handed neutrinos or as tools to lift the exotics and the authors explain a method to count their zero mode in the semi-local framework.


By the way, Marc Henneaux, Axel Kleinschmidt, Gustavo Lucena Gómez just wrote the most comprehensive paper yet explaining why the Hořava gravity is inconsistent. So far, the people who were looking at various solutions always focused on symmetric or otherwise special solutions.

But the present authors show that if one considers generic configurations, it's possible to prove that the lapse equals zero at infinity. For some coupling constants, they can solve much more about the system. They find out that the lapse must actually vanish everywhere. In other words, all constraints are second-class (and the time-reparameterization symmetry is a "trivial gauge symmetry"). Consequently, "everything" must dynamically equal to zero. The theory can contain no interesting physics.

Their derivation makes some previous observations that the phase space is "odd-dimensional" (and can't be paired) more comprehensible. The only way to fix the problem is to add new brutal constraints that oversimplify the theory and make its agreement with GR at long distances impossible.

I wonder whether all those people who have been producing not-quite-cautious papers with spherically symmetric and/or cosmological and/or black hole solutions will dare to notice that the theory actually doesn't contain any non-special solutions, or whether they will continue to push their increasingly dumb bandwagon and run rats through all kinds of mazes without paying attention to the actual conditions that are critical for the consistency of theories of gravity.

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