Warped Passages - Lisa Randall [156]
At Strings ’95, a conference held at the University of Southern California in March of that year, Edward Witten flabbergasted the audience by demonstrating that at low energies, a version of ten-dimensional superstring theory with strong coupling was completely equivalent to a theory that most people would have thought was entirely different: eleven-dimensional supergravity, the eleven-dimensional supersymmetric theory that contains gravity. And the objects in this equivalent supergravity theory interacted weakly, so perturbation theory could be usefully applied.
This meant, paradoxically, that you could use perturbation theory to study the original strongly interacting, ten-dimensional superstring theory. You would not use perturbation theory in the strongly interacting string theory itself, but in a superficially entirely different theory: weakly interacting, eleven-dimensional supergravity. This remarkable result, which Paul Townsend of Cambridge University had previously also observed, meant that despite their different packaging, at low energies, ten-dimensional superstring theory and eleven-dimensional supergravity were in fact the same theory. Or, as physicists would say, they were dual.
We can illustrate the idea of duality with our paint analogy. Suppose that we started off with blue paint, but then “perturbed” it by adding green. A good description of our paint mixture would then be blue paint with a hint of green. But suppose instead that the green paint we added wasn’t a small perturbation: suppose that we added an enormous amount of green paint. If that amount far exceeded the amount of the original blue paint, a better, “dual” description of the mixture would be green paint with a hint of blue. The preferred description entirely depends on the quantities of each color involved.
Similarly, a theory might have one description when a coupling of an interaction is small. But when that coupling is sufficiently large, perturbation theory is no longer useful in the original description. Nonetheless, in certain remarkable situations, the original theory can be completely repackaged in such a way that perturbation theory applies. That would be the dual description.
It’s as if someone presented you with the ingredients for a five-course meal. Even with all the ingredients, you might not know where to start. To make the meal work, you’d have to figure out which ingredients are intended for which course, how the spices interact with the food and with one another, and what to cook and when. But if caterers delivered the same ingredients pre-organized and prepared into salad, soup, appetizer, main course, and dessert, I expect that anyone could manage to turn that into a meal. With the same ingredients organized the right way, making a dinner goes from a complicated to a trivial problem.
Duality in string theory works in this way. Although strongly interacting, ten-dimensional superstring theory looked completely intractable, the dual description automatically organizes everything into a theory in which perturbation theory can be applied. Calculations which are difficult in one theory become manageable in the other. Even when the coupling in one theory is too big to use perturbation theory, the coupling of the other is sufficiently small to allow you to carry out perturbation calculations. However, we have yet to understand duality fully. For example, no one knows how to compute anything when the string coupling is neither very small nor very large. But when one of the couplings is either very small or very large (and the other is, respectively, very large or very small), then we can do calculations.
The duality of strongly coupled superstring theory and weakly coupled, eleven-dimensional supergravity theory tells you that you can calculate everything