Thermodynamics of the N = 2 * Flow

We discuss the thermodynamics of the N = 2, SU(N) gauge theory at large ’t Hooft coupling. The tool we use is the non-extremal deformation of the supergravity solution of Pilch and Warner (PW) [hep-th/0004063], dual to N = 4, SU(N) gauge theory softly broken to N = 2. We construct the exact non-extremal solution in fivedimensional gauged supergravity and further uplift it to ten dimensions. Turning to the thermodynamics, we analytically compute the leading correction in m/T to the free energy of the non-extremal D3 branes due to the PW mass deformation, and find that it is positive. We also demonstrate that the mass deformation of the non-extremal D3 brane geometry induces a temperature dependent gaugino condensate. We find that the standard procedure of extracting the N = 2 gauge theory thermodynamic quantities from the dual supergravity leads to a violation of the first law of thermodynamics. We speculate on a possible resolution of this paradox.