Thermodynamics of large-N super Yang-Mills theory AdS/CFT correspondence

The thermodynamics of d = 4, script N =4 supersymmetric SU(N) Yang - Mills theory is studied with particular attention paid to the perturbative expansion in the weak 't Hooft coupling regime and to the interpolation to the strong coupling regime thereof. The non-ideal gas effect to the free energy is calculated and found that leading- and next-to-leading-order corrections contribute with relative opposite signs. The Padé approximant method is adopted to improve fixed-order perturbative series and is found to decrease the free energy monotonically as the 't Hooft coupling parameter is increased. This may be regarded as an indication of a smooth interpolation of the thermodynamics between the weak and strong 't Hooft coupling regimes, as suggested by Maldacena's AdS/CFT correspondence.