Warped Passages - Lisa Randall [157]
The feature of this duality that makes it so incredible is that both descriptions involve only local interactions—interactions with nearby objects. Even if corresponding objects exist in both descriptions, duality is only a truly surprising and interesting phenomenon if both descriptions have local interactions. After all, a dimension is more than a collection of points: it is a way of organizing things according to whether they are nearby or far apart. A computer dump might contain everything I want to know and be equivalent to an organized set of files and documents, but it wouldn’t be a simple description unless the information were coherently organized with the relevant information contiguous. The local interactions in both the ten-dimensional superstring theory and the eleven-dimensional supergravity theory are what makes the dimensions in both theories—and therefore the theories themselves—meaningful and useful.
The equivalence between ten-dimensional superstring theory and eleven-dimensional supergravity vindicated Paul Townsend at Cambridge and Michael Duff, then at Texas A&M. For a long time, string theorists had largely rebuffed and maligned their work on eleven-dimensional supergravity—they couldn’t understand why Duff and Townsend were wasting their time with this theory when string theory was so obviously the physics of the future. After Witten’s talk, string theorists had to concede that eleven-dimensional supergravity was not only interesting, it was equivalent to string theory!
I realized how much attention this surprising result about duality was receiving when I was on a plane returning from London. A fellow passenger, who turned out to be a rock musician, saw that I was reading some physics papers. He came over and asked me whether the universe had ten or eleven dimensions. I was a little surprised. But I did answer and explained that in some sense, it is both. Since the ten-and eleven-dimensional theories are equivalent, either one can be considered correct. The convention is to give the number of dimensions in whichever of the theories has weakly interacting strings and thus a lower physical value of the string coupling.
But unlike the couplings associated with Standard Model forces, whose strength we can measure, we don’t yet know the size of the string coupling. It might be weak, in which case perturbation theory can be applied directly; or it might be strong, in which case you would be better off using perturbation theory in the dual description. Without knowing the value of the string coupling, we have no way of knowing which, if either, of the two descriptions is the simpler way to describe string theory as it applies to the world.*
And there were more duality surprises at Strings ’95. Until then, most string theorists had thought there were five versions of superstring theory, each of which included different forces and interactions. At Strings ’95, Witten (and before that, Townsend and another British physicist, Chris Hull) demonstrated dualities between pairs of versions of superstring theory. And over the course of 1995 and 1996, string theorists showed that all these versions of ten-dimensional theories were dual to one another, and, furthermore, were dual to eleven-dimensional supergravity. Witten’s talk had triggered a veritable duality revolution. With the extra input from the nature of branes, the five apparently distinct superstring theories were shown to be the same theory in different guises.
Because the various versions of string theory are actually the same, Witten concluded that there must exist a single theory that encompasses eleven-dimensional supergravity and the different manifestations of string theory, whether or not they contain