Thermodynamics of Large - N Super Yang - Mills Theory and AdS / CFT Correspondence 1

Thermodynamics of d = 4, N = 4 supersymmetric SU(N) Yang-Mills theory is studied with particular attention on perturbative expansion at weak ‘t Hooft coupling regime and interpolation to strong coupling regime thereof. Non-ideal gas effect to free-energy is calculated and found that leadingand next-to-leading-order corrections contribute with relative opposite signs. Padé approximant method is adopted to improve fixed-order, perturbative series and is found to decrease free-energy monotonically as ‘t Hooft coupling parameter is increased. This may be regarded as an indication of smooth interpolation of thermodynamics between weak and strong ‘t Hooft coupling regimes, as suggested by Maldacena’s AdS/CFT correspondence. Work supported in part by KOSEF Interdisciplinary Research Grant 98-0702-07-01-5 and SRC Program, KRF International Collaboration Grant, Ministry of Education Grant 98-015-D00054, and The Korea Foundation for Advanced Studies Faculty Fellowship.