Warped Passages - Lisa Randall [161]
Let’s now see how string theory can confine particles and forces on branes. Imagine that there is only one D-brane, suspended somewhere in a higher-dimensional universe. Because, by definition, both ends of an open string must be on a single D-brane, this D-brane would be where all open strings begin and end. The ends of each open string wouldn’t be stuck in any particular location, but they would have to lie somewhere on the brane. Like train tracks that confine wheels but allow them to roll, the branes act as fixed surfaces in which the ends of the string are confined but can nonetheless move.
Because the vibrational modes of open strings are particles, the modes of an open string with both ends confined to a brane are particles that are confined to this brane. Those particles would travel in and interact only along the dimensions spanned by the brane.
It turns out that one of these particles arising from a brane-bound string is a gauge boson that can communicate a force. We know this because it has the spin of a gauge boson (which is 1), and because it interacts just as a gauge boson should. Such a brane-bound gauge boson would communicate a force that would act on other brane-bound particles, and calculations show that the particles on the receiving end are always charged under this force. In fact, the endpoint of any string ending on the brane would act like a charged particle. The presence of the brane-bound force and these charged particles is what tells us that a D-brane of string theory comes “loaded” with charged particles and a force that acts upon them.
In setups with more than one brane, there will be more forces and more charged particles. Suppose, for example, that there were two branes. In that case, in addition to the particles confined to each of the branes, there would be a new type of particle arising from strings whose two ends were on the two different branes (see Figure 70).
Figure 70. A string that begins and ends on a single brane can give rise to a gauge boson. A string with each end on a different brane gives rise to a new type of gauge boson. When the branes are separated, the gauge boson has nonzero mass.
It turns out that if the two branes are separated from each other in space, the particles associated with the string that extends between them will be heavy. The mass of the particles arising from the vibrational modes of this string grows with the distance between the branes. This mass is like the energy that gets stored when you stretch a spring—the more it is stretched, the more energy it contains. Similarly, the lightest particle that arises from a string stretched between two branes will have a mass that increases in proportion to the brane separation.
However, when a spring is relaxed in its rest position, it doesn’t store any energy. Similarly, if the two branes are not separated—that is, if they are in the same place—the lightest string particle arising from the string with an end on each brane is massless.
Let’s now assume that the two branes coincide, so that they produce some massless particles. One of these massless particles would be a gauge boson—not one of the gauge bosons that arises from strings with both ends on a single brane, but a distinct, new one. This new massless gauge boson, which arises only when there are coincident branes, communicates a force that acts on particles on either one or both of the two branes. Furthermore, as with all other forces, the forces on the brane are associated with a symmetry. In this case the symmetry transformation would be the one that exchanges the two branes (which a punning Igor might enjoy).29
Of course, if two branes really were in the same place, you might think