Thermodynamics of spinning branes and their dual field theories

We present a general analysis of the thermodynamics of spinning blackp-branes of string and M-theory. This is carried out both for theasymptotically-flat and near-horizon case, with emphasis on the latter. Inparticular, we use the conjectured correspondence between the near-horizonbrane solutions and field theories with 16 supercharges in various dimensionsto describe the thermodynamic behavior of these field theories in the presenceof voltages under the R-symmetry. Boundaries of stability are computed for allspinning branes both in the grand canonical and canonical ensemble, and theeffect of multiple angular momenta is considered. A recently proposedregularization of the field theory is used to compute the correspondingboundaries of stability at weak coupling. For the D2, D3, D4, M2 and M5-branesthe critical values of Omega/T in the weak and strong coupling limit areremarkably close. Finally, we also show that for the spinning D3-brane the treelevel R^4 correction supports the conjecture of a smooth interpolating functionbetween the free energy at weak and strong coupling.Comment: 59 pages, JHEP class. Minor typos corrected, added remark on positivity of temperature, Sec. 6.1 improved, references adde