Thermodynamic stability and phases of general spinning branes

We determine the thermodynamic stability conditions for near-extreme rotating D3, M5, and M2-branes with multiple angular momenta. Critical exponents near the boundary of stability are discussed and compared with a naive field theory model. From a partially numerical computation we conclude that outside the boundary of stability, the angular momentum density tends to become spatially inhomogeneous. Periodic euclidean spinning brane solutions have been studied as models of QCD. We explain how supersymmetry is restored in the world-volume field theory in a limit where spin becomes large compared to total energy. We discuss the hierarchy of energy scales that develops as this limit is approached.