Thermodynamics of Spinning Branes and their Dual Field Theories

TL;DR

The paper develops a unified framework for the thermodynamics of spinning black p-branes, linking asymptotically flat and near-horizon regimes to dual 16-supercharge field theories. It derives general spinning brane solutions, computes their thermodynamics, and investigates stability in both grand canonical and canonical ensembles, including multiple angular momenta. The authors compare strong-coupling supergravity results with weak-coupling field theory, providing evidence that critical Omega/T values stay close across limits and demonstrating a smooth interpolation via higher-derivative corrections for D3-branes. They also validate the Euclidean action approach by reproducing the Gibbs free energy and discuss the implications for the AdS/CFT-type dualities with R-symmetry deformations.

Abstract

We present a general analysis of the thermodynamics of spinning black p-branes of string and M-theory. This is carried out both for the asymptotically-flat and near-horizon case, with emphasis on the latter. In particular, we use the conjectured correspondence between the near-horizon brane solutions and field theories with 16 supercharges in various dimensions to describe the thermodynamic behavior of these field theories in the presence of voltages under the R-symmetry. Boundaries of stability are computed for all spinning branes both in the grand canonical and canonical ensemble, and the effect of multiple angular momenta is considered. A recently proposed regularization of the field theory is used to compute the corresponding boundaries of stability at weak coupling. For the D2, D3, D4, M2 and M5-branes the critical values of Omega/T in the weak and strong coupling limit are remarkably close. Finally, we also show that for the spinning D3-brane the tree level R^4 correction supports the conjecture of a smooth interpolating function between the free energy at weak and strong coupling.