Warped Passages - Lisa Randall [154]
These small branes, like more familiar macroscopic objects, have a mass that grows with their size. More of something (like lead pipe or dirt or cherries) is heavier, and less of it is lighter. Because a brane wrapped around a tiny region of space is so small, it will also be extremely light. And Andy’s calculations showed that in the extreme case when the brane is as minuscule as you can imagine, this tiny brane looks like a new massless particle. Andy’s result was crucial in that it showed that even the most basic hypothesis of string theory—that everything arises from strings—is not always correct. Branes, too, contribute to the particle spectrum.
Joe’s remarkable observation of 1995 was that these new particles that arise from tiny p-branes could also be explained with D-branes. In fact, in his paper establishing the relevance of D-branes, Joe showed that D-branes and p-branes were actually the same thing. At energies where string theory makes the same predictions as general relativity, D-branes morph into p-branes. Joe and Andy, though they didn’t realize it at first, had actually been studying the same objects. This result meant that the significance of D-branes could no longer be questioned: they were no less important than the p-branes that had preceded them, and those p-branes were essential to the string theory spectrum of particles. Furthermore, there is a beautiful way to understand why p-branes are equivalent to D-branes. It is based on the subtle and important notion of duality.
Mature Branes and Duality
Duality is one of the most exciting concepts of the last ten years in particle physics and string theory. It has played a major role in recent advances in both quantum field theory and string theory, and, as we will soon see, it has especially important implications for theories with branes.
Two theories are dual when they are the same theory with different descriptions. In 1992 the Indian physicist Ashoke Sen was one of the first to recognize duality in string theory. In his work, which followed up the idea of duality that the physicists Claus Montonen and David Olive had originally introduced in 1977, he showed that a particular theory remained exactly the same if the particles and strings of the theory were interchanged. In the 1990s, the Israeli-born physicist Nati Seiberg, who was then at Rutgers University, also demonstrated remarkable dualities between different supersymmetric field theories with superficially different forces.
To understand duality’s significance, it helps to know a little about how string theorists generally do calculations. String theory’s predictions depend on the string’s tension. But they also depend on the value of a number called the string coupling, which determines the strength with which strings interact. Do they brush past each other, corresponding to a weak coupling, or do they collude about their mutual fates, corresponding to a strong coupling? If we knew the value of the string coupling, we could study string theory for only that particular value. But because we don’t yet know the value of the string coupling, we can hope to understand the theory only when we can make predictions for any string interaction strength. Then we can find out which one works.
The problem was that since the inception of string theory, the strongly coupled theory had appeared to be intractable. In the 1980s only string theory with weakly interacting strings was understood. (I’m using the adjective “weak” to describe the strength of string interactions, but don