and because I think that it is definitely an interesting paper, let me say a couple of words.
Imagine that you take a type II string theory and compactify it down to 8 dimensions, on a two-dimensional genus "g" Riemann surface.
Well, unless "g=1", it is a non-conformal theory, so you will have to deal with a time-dependent background. Let's not worry. Let's assume the string coupling to be weak throughout the story.
Imagine that you start with a genus 2 Riemann surface. It can degenerate into two genus 1 Riemann surfaces connected by a thin tube. The circle wrapped around this tube is homologically trivial, and you can show that the fermions will be antiperiodic around it: it will be a Scherk-Schwarz/Rohm compactification on a thermal circle. The reason for the antiperiodicity is the same like the reason that the closed strings in the NS-NS sector must have antiperiodic boundary conditions for the fermions assuming that the corresponding operators in the "z" plane don't introduce any branch cuts.
OK, imagine that the tube is very long. Because of the antiperiodic boundary conditions, the sign of the GSO condition in the sectors with odd windings is reverted, and one can find some tachyons there assuming that the radius is small enough so that the winding is not enough to make the squared mass positive. Equivalently, one can T-dualize along the circumference of the tube to obtain some sort of type 0 theory which has a bulk tachyon if the radius in the type 0 picture is large enough. Go exactly near the point where the first tachyon in the "w=1" sector starts to evolve. It's the first perturbative instability you encounter.
These guys then argue that the most obvious time evolution will take place. The tachyons start to get condensed, and the handle will pinch off. It can be seen as a perturbative instability although it is probably continuously connected to the non-perturbative stability called the Witten bubble, and they use various CFT techniques, Ricci flows, RG flows, N=1 and N=2 worldsheet supersymmetry to study the process quantitatively. They argue that the two ends of the tube don't talk to each other - the strings can't propagate through the critical region where the topology change takes place. I am not gonna write the math here because you can open the paper.
Such a process can reduce the genus of a Riemann surface. Recall the picture with Brian Greene's breakfast on PBS/NOVA: the topology of the coffee cup and the doughnut are identical, but once Brian bites doughnut, it is going to become a sphere. In this case, the TV program is exact, not just a lower-dimensional analogy of the conifold transition. ;-)
The same process, however, can divide a higher genus Riemann surface into pieces that don't interact at all. The world decays into pieces - baby universes and similar stuff. A lot of interesting stuff happens from the low-energy effective theory viewpoint - doubling of gravity, decoupling of various modes, gaps emerging and disappearing, and many other things. Note that spacetime supersymmetry is broken, but one can arrange the parameters of the geometry in such a way that the evolution is more or less controllable.
I still believe that similar kinds of topology changing transitions may eventually destabilize or eliminate most of the "landscape". If you start with a too convoluted Calabi-Yau space with fluxes, there will be many modes how it can decay - it is potentially able to split into two (or more) Calabi-Yau pieces. Instead of the 2-dimensional handles of the cylindrical type, there may be many higher-dimensional analogues of the cylinder although most of us so far seem to have trouble to find working higher-dimensional examples. Such processes do not have to be too likely, but there are just many channels in which such a complicated Calabi-Yau space can decay - the number of channels is large because the number of "simpler" minima in the landscape is claimed to be large as well. This largeness is, I believe, self-destructive for the landscape.
My intuition is that such a decay tends to simplify the homology of both final products - i.e. reduce their Hodge numbers. This is a reason to believe that the Calabi-Yaus with very small Hodge numbers will be preferred. Braun, He, Ovrut, Pantev have found a quasi-unique heterotic standard model based on a Calabi-Yau with h^{1,1}=h^{2,1}=3. Three is the smallest positive integer after one and two - a pretty good choice. Assuming that there is something right about this and previous paragraph, Braun et al. have a pretty good chance that they have found the theory of everything. ;-)
Meanwhile, Adams et al. have made useful steps to understand tachyons in string theory. Note that these new understood tachyons start to look like bulk tachyons. The first understood tachyons were open tachyons (Sen and others); then people (APS; but also Headrick) continued with the closed string twisted tachyons; now they're getting into the bulk.
Comments welcome.
