Black holes and the SYM phase diagram

Making combined use of the matrix and Maldacena conjectures, the relation between various thermodynamic transitions in super Yang-Mills (SYM) theory and supergravity is clarified. The thermodynamic phase diagram of an object in DLCQ M theory in four and five non-compact space dimensions is constructed; matrix strings, matrix black holes, and black $p$-branes are among the various phases. Critical manifolds are characterized by the principles of correspondence and longitudinal localization, and a triple point is identified. The microscopic dynamics of the matrix string near two of the transitions is studied; we identify a signature of black hole formation from SYM physics.