5d Black holes, wrapped fivebranes and 3d Chern-Simons Super Yang-Mills

We study extremal and non-extremal generalizations of the regular non-abelian solution found by Chamseddine and Volkov in 5d N=4 gauged supergravity, which has been shown by Maldacena and Nastase to describe a system of NS5-branes wrapping an S dual to three-dimensional U(N) N = 1 supersymmetric Yang-Mills with Chern-Simons coupling k = N 2 . All black hole solutions have a temperature larger than the Hagedorn temperature Tc of the little string theory and their entropy decreases as the temperature increases. This is a sign that the system is thermodynamically unstable above Tc. We have also found an analytical solution describing NS5-branes wrapped on a constant radius S and involving a linear dilaton. Its non-extremal generalization has a temperature equal to 2Tc. ∗Research supported in part by the CTP and the LNS of MIT and the U.S. Department of Energy under cooperative research agreement # DE-FC02-94ER40818. G. B. is also supported in part by the INFN “Bruno Rossi” Fellowship.