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تسجيل مستخدم جديد${cal N}=4$ supersymmetric Yang-Mills thermodynamics to order $lambda^2$
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We calculate the resummed perturbative free energy of ${cal N}=4$ supersymmetric Yang-Mills in four spacetime dimensions ($text{SYM}_{4,4}$) through second order in the t Hooft coupling $lambda$ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over $text{SYM}_{4,4}$ ring diagrams. Non-analytic terms at ${cal O}({lambda}^{3/2}) $ and $ {cal O}({lambda}^2 loglambda )$ are generated by dressing the $A_0$ and scalar propagators. The gauge-field Debye mass $m_D$ and the scalar thermal mass $M_D$ are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of $text{SYM}_{4,4}$ to ${cal O}(lambda^2)$. We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Pad{e} approximant that interpolates between the weak-coupling result and the large-$N_c$ strong-coupling result. Our results suggest that the ${cal O}(lambda^2)$ weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for $0 leq lambda lesssim 2$.
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