Warped Passages - Lisa Randall [165]
Figure 72. Schematic drawing of the Hořava-Witten braneworld. Two branes with nine spatial dimensions (represented schematically by two-dimensional branes) are separated along the eleventh spacetime dimension (the tenth spatial dimension). The bulk includes all spatial dimensions: those nine that extend in the spatial directions along the two branes, and the additional one that extends between them.
In fact, the HW braneworld didn’t just have the same forces as the heterotic string—it was the heterotic string, albeit with strong string coupling. This is another example of duality. In this case, an eleven-dimensional theory with two branes bounding the eleventh dimension (the tenth dimension of space) is dual to the ten-dimensional heterotic string. That is to say, when the interactions of the heterotic string are very strong, the theory is best described as an eleven-dimensional theory with two boundary branes and nine spatial dimensions. This is not unlike the duality between ten-dimensional superstring theory and eleven-dimensional supergravity that was discussed in the previous chapter. But in our present example, the eleventh dimension is not rolled up, but is instead bounded between two branes. Once again, an eleven-dimensional theory can be equivalent to a ten-dimensional one, albeit when one theory has strong interactions and the other has feeble ones.
Of course, even if Standard Model particles are confined to a brane, the theory would still have more dimensions than we see around us. If the Hořava-Witten braneworld is to correspond to reality, six of its dimensions must be unseen. Hořava and Witten assumed that six dimensions were curled up into a tiny Calabi-Yau shape.
Once six dimensions are curled up, you can think of the HW universe as a five-dimensional effective theory with four-dimensional boundary branes. This picture of a five-dimensional universe with two boundary branes is an interesting one that many physicists have investigated. Raman and I applied some of the techniques that two physicists, Burt Ovrut and Dan Waldram, used to study the HW effective theory to the different five-dimensional theories that I’ll discuss in Chapters 20 and 22.
One fascinating element of the Hořava-Witten braneworld is that it can accommodate not only the Standard Model particle and forces, but also a full Grand Unified Theory. And because gravity originates in higher dimensions, it’s possible for gravity and other forces to have the same strength at high energy in this model.
The HW braneworld illustrates three reasons why braneworlds can matter for real-world physics. First, it involves more than a single brane. This means that it can contain forces and particles that interact with each other only weakly because of the distance between the two branes on which they are bound. The only way that particles confined to different branes can communicate is through common interactions with bulk particles. This first feature will be significant in the sequestering models that we’ll look at in the next chapter.
The second important braneworld feature is that any braneworld introduces new length scales into physics. These new scales, like the size of the additional dimensions, might be relevant to unification or the hierarchy problem. Problems in both of these theories center around why there should be very different energy and mass scales in a single theory, and why quantum effects don’t tend to equate the two.