Well, my colleagues (Eugene Lim, I-Sheng Yang, Pontus Ahlqvist, Saswat Sarangi, and Brian Greene) and I have finally put out our paper on flux vacua and stringy tunneling. Take a look:
It’s rather long, although we tried to be very detailed in our appendices and have included some calculations that are rather standard (the Klebanov-Strassler stuff along with the near-conifold expansions) for completeness.
There are two basic themes in this work:
1) How do we efficiently find vacua for tractable flux compactifications, and what are some of the relationships between them?
2) What are the details of the tunneling processes that might take you from one vacuum to another one that is smoothly connected via the potential?
I’ll now repeat a story that has been told many times before. String theory is most naturally formulated in ten dimensions. This leads to the obvious problem that we only observe four dimensions, three spatial dimensions (jump up and down, move left and right, forward and back) and one time direction (get older). This leads to one of the key questions in the field, “who’re you gonna believe? String theory or your lyin’ eyes?”
Well, the question doesn’t necessarily have to be either/or—you probably should believe your lyin’ eyes (ish), but that doesn’t rule string theory out. In fact, the extra six dimensions that seem extraneous and unwanted can be rolled up into certain types of shapes (Calabi-Yau manifolds and related objects). In this way they can be made very small, so small, we wouldn’t be able to detect them—at least not up until now. An added bonus is that if you roll them up the right way, you can get physics that is remarkably similar to the kind observed by us both gravitationally and in particle physics.
This business of rolling up dimensions isn’t as abstract as it sounds. Brian Greene has a nice explanation of it in terms of a garden hose. When you are far away, the hose looks like a long one dimensional line. But when you zoom in, you see that there is a rolled-up dimension that actually makes the hose a cylinder.
Note however that I stipulate that the physics is *similar* to the stuff that we already observe—similar but not exactly the same. In fact, if you do just as I have described, the extra dimensions still pose some problems. Think about the garden hose: the size of the rolled up dimension is an important input, and in string theory, the sizes of certain handles and holes in these more complicated Calabi-Yau shapes as well as the overall size of the shape itself are not for you to simply declare by fiat. Instead, one hopes that physics itself should cause these sizes to stabilize in some manner. Thus, we allow these parameters to become fields—or since it’s effectively the same thing—particles in our 4D universe. The size that they stabilize at is going to be related to the mass of these particles—bigger masses means smaller sizes.
That is *if* they stabilize at all. The problem with rolling up the extra dimensions in string theory on just a Calabi-Yau manifold is that these new particles (and there are potentially hundreds of them) actually don’t develop a mass. This means we should be detecting them if they exist. This of course is a problem.
But there are ways out. The reason that these particles don’t develop a mass is because there are no forces that act on the rolled up geometry to guide the sizes of these holes and handles. String theory however has an answer to that: it contains precisely the ingredients you would need to put fields similar to electric and magnetic fields through these shapes in just such a way that these new particles gain masses. The shapes settle at a size that minimizes the energy needed to balance out these generalized electric and magnetic fields. These fields through the rolled up shapes are called “fluxes” and the particles that represent the sizes of these shapes are called “moduli fields.” The whole business is called flux compactification of string theory.
I have to run and this is a natural place to pause. In the next part, I will try to explain what it is that my colleagues and I do in our paper.