Duality cascade and oblique phases in non-commutative open string theory

We investigate the complete phase diagram of the decoupled world-sheet theory of (P, Q) strings. These theories include 1+1 dimensional super Yang-Mills theory and non-commutative open string theory. We find that the system exhibits a rich fractal phase structure, including a cascade of alternating supergravity, gauge theory, and matrix string theory phases. The cascade proceeds via a series of SL(2, ℤ) S-duality transformations, and depends sensitively on P and Q. In particular, we find that the system may undergo multiple Hagedorn-type transitions as the temperature is varied.