Warped Passages - Lisa Randall [152]
Some branes extend in three dimensions, but others extend in four or five or more dimensions. In fact, string theory contains branes that extend in any number of dimensions up to nine. The string theory convention for labeling branes is to use the number of dimensions of space—not of spacetime—in which they extend. For example, a 3-brane is a brane that extends through three dimensions of space (but four dimensions of spacetime). When we come to look at the consequences of branes for the visible world, 3-branes will be very important. However, for the applications of branes discussed in this chapter, branes with other numbers of dimensions will also play a role.
Different types of brane arise in string theory. They are distinguished not only by their dimensionality—the number of dimensions in which they extend—but also by their charges, their shape, and an important characteristic called tension (which we’ll get to soon). We don’t know whether branes exist in the real world, but we do know the types of brane that string theory says are possible.
Branes were just a curiosity at the time they were discovered. Back then, no one saw any reason to include branes that interacted or moved. If strings interacted only weakly, as string theorists initially assumed, D-branes would be so taut that they would just sit there and not contribute to string motion or interactions. And if branes don’t respond to strings in the bulk, they would just be an unnecessary complication. They would be a place or location, but they would be no more relevant to the motions and interactions of strings than the Great Wall of China is to your daily existence. Moreover, physicists didn’t want to include branes in a physical realization of string theory because branes violated their intuition that all dimensions are created equal. Branes distinguish certain dimensions—those along the brane are different from those that extend off it—whereas the known laws of physics treat all directions the same. Why should string theory be different?
We also expect physics at any one point in space to be the same as it is at any other. But branes don’t respect this symmetry either. Although branes extend infinitely far along some dimensions, they are situated at a fixed position in the other directions. That is why they don’t span all of space. But in those directions in which the brane’s position is fixed, an inch from the brane is not the same as a yard or a half-mile from the brane. Imagine a brane that was drenched in perfume. You would definitely be able to tell whether you were near it or far from it.
For these reasons, string theorists initially ignored branes. But about five years after branes were discovered, their status in the theoretical community dramatically improved. In 1995 Joe Polchinski irreversibly changed the course of string theory when he showed that branes were dynamical objects that were integral to string theory and were likely to play a critical role in its ultimate formulation. Polchinski explained what types of D-brane are present in superstring theory, and demonstrated that these branes carry charge28 and therefore interact.
Moreover, the branes in string theory have finite tension. Brane tension is akin to the tension of the surface of a drum that returns to its taut position after you pinch it or punch it. If a brane’s tension