Stabilized heterotic Calabi-Yau shapes

Lara Anderson, an expert in Japanese martial arts and an ex-Rhodes scholar, and three collaborators - James Gray, Andres Lukas, and Burt Ovrut - have released a very interesting preprint called

Stabilizing All Geometric Moduli in Heterotic Calabi-Yau Vacua

Your humble correspondent belongs among the heterotic partisans. I think that the heterotic string producing a supersymmetric GUT-based extension of the Standard Model remains the most well-motivated scenario how string theory contains the world around us - even though some other, more contemporary scenarios came pretty close to it.




However, there has been a problem with the heterotic compactifications: most scalar fields parameterizing the shape of the Calabi-Yau internal manifold were remaining exact massless moduli. That would leave the shape of the manifold undetermined, allow the low-energy parameters of particle physics to evolve, and it would lead to new long-range forces, too.

In the favorite scenario of the landscape partisans, the type IIB flux vacua, the stabilization of the moduli is usually achieved by the KKLT prescription: the fluxes play an important role. However, the corresponding fluxes can't be turned on in the heterotic string. There are no Ramond-Ramond fields at all and the Neveu-Schwarz B-field is severely constrained by the Calabi-Yau condition.

Finally, these physicists have figured out the right ally that may be responsible for the stabilization. Of course, it's the E8 x E8 gauge field. With a right bundle, all geometric moduli are perturbatively (!) stabilized. That only leaves the dilaton (redefined by a function of the Kähler parameters0 as the adjustable scalar field.

(The full stabilization has also been achieved in the G2 holonomy compactifications of M-theory.)

When this procedure is done, one actually ends up with a more promising result than the KKLT type IIB flux vacua because the classical cosmological constant is just zero, without any need to adjust the fluxes. Non-perturbative effects - namely gaugino condensation and instantons - may stabilize the rest and their studied in the later parts of the new paper.

Concerning the cosmological constant issue, I have probably said and written the same thing many times, but let me try to say it differently.

The cosmological constant seems unnaturally tiny. There is no known satisfactory solution that would really explain why it is so small, without using the existence of observers as a selection criterion. The anthropic attitude is to conclude that such a solution can't exist, so the earlier we give the search up, the better. Using a large number of random vacua - much more than 10^{120} of them - is enough to adjust the value to anything.

The non-anthropic solutions don't quite get to the figure 10^{-123} for the cosmological constant but they can get 10^{-60} for low-energy supersymmetry. This is not a full solution but I still think that it is a half-solution. Using a class of vacua that achieve such things naturally reduces the amount of fine-tuning e.g. from one part in 10^{120} to one part in 10^{60} which is a good thing.

So even if there has to be some anthropic selection somewhere at the end, I think that the need for such a selection should be as small as possible, and the active role for such an anthropic selection should be delayed as much as possible. The later we need this help, the better.