Resummed perturbative free energy of N=4 SYM is calculated to order λ^{5/2} at finite temperature, yielding a UV and IR finite result after including ring diagrams.
For example, if a term has the productδ p0δp0+k0 then a transfor- mationK→−K−Pcan be used to rewrite it so that the Kronecker deltas have the formδ p0δk0
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${\cal N}=4$ supersymmetric Yang-Mills thermodynamics to order $\lambda^{5/2}$
Resummed perturbative free energy of N=4 SYM is calculated to order λ^{5/2} at finite temperature, yielding a UV and IR finite result after including ring diagrams.