The previous blog article about the heterotic minimal supersymmetric standard models is here.
One of the usual complaints against the traditional line of superstring model building is that there is no huge landscape of such vacua, which is why you can't solve the cosmological constant problem.
This is a pseudoargument because there exists no quantitative evidence that the cosmological constant problem can't be resolved in a scientific way.
Burt Ovrut and Volker Braun propose their picture here:
Inside the visible E_8 on their favorite pure MSSM Calabi-Yau manifold, they use their latest pure MSSM bundle that leads to the correct minimal MSSM spectrum. The corresponding bundle for the hidden E_8 that would cancel the anomalies has been known to be unstable. Instead, Ovrut and Braun use a trivial bundle for the hidden E_8 and cancel the anomalies by M5-branes and anti-M5-branes that live in the bulk, in between the two domain walls.
If you only used M5-branes but no anti-M5-branes, you would obtain a supersymmetric AdS vacuum whose cosmological constant is of order -10^{-16} M_{Pl}^4 - which is large and has a wrong sign - as they show in two simplified but nevertheless pretty complex models. However, when you use both M5-branes as well as anti-M5-branes, you may obtain positive and perhaps even semi-realistic values of the vacuum energy as long as you adjust the Kähler moduli to appropriate values. At these values, the visible bundle is slope-stable, too, which is a good news.
At the beginning of their paper, they review their best and minimal model. They advocate the opinion that gaugino condensation in the hidden sector, even though it is popular, is not a phenomenologically attractive way to break SUSY in heterotic M-theory. This is why they decide that M5-branes and anti-M5-branes whose curves are fixed by the anomaly cancellation are a better way to break SUSY "explicitly" (of course that the breaking is still "spontaneous" from the viewpoint of the full string/M-theory).
In their simplified analysis, they neglect the bundle moduli but show the stabilization of the dilaton, complex structure moduli, and Kähler moduli.
Numbers
Imagine that you believe that they are converging to the theory of everything. What are the relevant scales?
- the coupling alpha_{GUT} = 1/25 near the Planck scale
- the Planck scale is around the usual 10^{19} GeV
- the Calabi-Yau radius scale is around the GUT scale, 10^{16} GeV - the GUT and Calabi-Yau scales coincide because the momentum modes at the Calabi-Yau scale that feel the Wilson lines can be interpreted as the GUT-breaking Higgses
- the eleventh dimension is longer, 1/R is around 10^{14} GeV that can already be called an intermediate scale, which is why the theory is five-dimensional above this scale and below the GUT scale
In Ovrut and Braun's framework, the realistic values of the cosmological constant may be obtained from very reasonable numbers. The tiniest number they need to use is "Vscript_5bar" - the volume of a one-complex dimensional surface on which the anti-M5-brane is wrapped. Recall that one needs to get a cosmological constant that is 120 orders of magnitude below the Planck scale, so you might think that you need a ridiculously small two-cycles on which the anti-M5-brane is wrapped.
However, their calculation shows that you only need a two-cycle whose area is about 10^{-7} in the Calabi-Yau area unit (the unit of area is the third root of the volume of the Calabi-Yau manifold). This more or less reasonable number leads to the observed value of the cosmological constant.
Snow has returned to Cambridge...
