Friday, April 30, 2010

String Axiverse

One year ago, five phenomenologists have introduced the notion of the String Axiverse, a typically stringy realization of a set of axions whose masses are distributed quasi-uniformly on the log scale.

Asimina Arvanitaki, Savas Dimopoulos, Sergei Dubovsky, Nemanja Kaloper, and John March-Russell called the paper simply
String Axiverse.
Today, three string theorists - namely Bobby Samir Acharya, Konstantin Bobkov, and Piyush Kumar - posted one of the most interesting follow-ups:
An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse
which gives a natural realization of the axiverse within string theory, therefore confirming the prophesies of the authors above.

Recall that axions are pseudoscalar fields that (may) explain why the theta-angle in QCD is so small - if they're light enough.

In string/M-theory, many axions are determined topologically because they're the integrals of p-form tensor fields over cycles of the compact manifold. And because the extra-dimensional manifolds may be very complex and resemble a "turbulent pattern", you may find qualitatively self-similar structures in it, indicating that physics wants to be uniformly distributed on the logarithmic scale - something we know to be "nearly" the case for the Yukawa couplings etc.

To be honest, the right explanation why the axion masses cover the interval logarithmically is actually not the self-similarity of the manifolds themselves: it's that the masses come from instantons - whose contributions are exponentials with exponents that end up being quasi-uniformly distributed on the linear scale. ;-)

Well, I actually find it more likely that the compact manifold of extra dimensions is "simple" in some proper definition of the word (which would indicate a "minimum" number of such instantons as well) but it's just my belief - or prejudice, if you wish - and it's surely interesting to consider the other possibility that it's complicated and the - empirically encouraging - observation that physics tends to be uniformly distributed on the log scale is surely a positive argument in favor of a complex compactification.

If it's complicated, many consequences follow. Acharya et al. show them in a robust context of M-theory (although there's not much extra-dimensional geometry and model building in this paper; they refer to older ones). The scenario has lots of observable predictions: for example, it says that Planck can see no tensor modes.

Using mostly SUGRA formalism, Acharya et al. argue that M-theoretical (and some closely linked type IIB) compactifications stabilized at non-supersymmetric minima produce axions between 10^{-30} eV all the way to 10^{12} GeV or so, satisfy various constraints, and require no anthropic fine-tuning for a certain choice of the axion decay constant and the lightest axion mass.

1 comment:

  1. Aren't the topological constraints fixed by the possible covering spaces of the base manifold?

    Anyway the point of this whole thing to me is, if what they assume is true, then the mass distribution is fixed, and there is no room for further adjustment.