Black holes and five-brane thermodynamics

The phase diagram for Dp-branes in hi theory compactified on T-4, T-4/Z(2), T-5, and T-6 is constructed. As for the lower-dimensional tori considered in our previous work [E. Martinec and V. Sahakian, Phys. Rev. D 59, 124005 (1999)], the black brane phase at high entropy connects onto matrix theory at low entropy; we thus recover all known instances of matrix theory as consequences of the Maldacena conjecture. The difficulties that arise for T-6 are reviewed. We also analyze the D1-D5 system on T-5; we discuss its relation to matrix models of M5-branes, and use spectral how as a tool to investigate the dependence of the phase structure on angular momentum. [S0556-2821(99)03316-0].