>>11420264There really aren't so many prerequisites, the difficulties in string theory are the alien physics, not the mathematics. Aside from standard topics for physics, you need to know all the Lie Algebras well, not just SO(3), SU(3), SU(5). The natural path here is through the SU(5) SO(10) E6 guts, and you can learn this from Green-Schwarz-Witten. You need to know homology/cohomology intuitively, and a small amount of algebraic geometry, just to relate the compactification geometry to the physics. But the barriers to learning the theory are developing a physical intuition for such alien things as strings.
For this, you need to learn the complex analytic things that motivated the original discovery. You need to an intuition for analytic continuation, this is standard undergraduate stuff, but the physicist intuition is more developed--- you can read Gribov's book "The Theory of Complex Angular Momentum", along with Mandelstam's articles on the Analytic S-matrix, and those of others throughout the sixties. This is the most difficult thing--- understanding the analytic S-matrix stuff, and this is not something that rigorous mathematics is going to help very much with, and it is not even current in physics departments anymore, it is just buried.
After this. the remaining mathematics of string theory is developed most straightforwardly by learning the theory from physics sources. The Kac-Moody algebras, the conformal algebras, the mirror symmetry, even the Ricci flow, these are all things that were developed first within string theory. The flow of ideas here has been nearly entirely from physics into mathematics, with a few exceptions that are still more clearly described in the physics literature.
