Padé interpolation between NLO weak- and strong-coupling results places the thermal N=4 SYM transition region at 't Hooft coupling λ roughly between 3 and 14.
Finite coupling corrections to holographic predictions for hot QCD
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abstract
Finite 't Hooft coupling corrections to multiple physical observables in strongly coupled $N=4$ supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the 't Hooft coupling $\lambda$. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Although large $\lambda$ expansions for quasinormal mode frequencies are notably less well behaved than the expansions of other quantities, we find that a partial resummation of higher order corrections can significantly reduce the sensitivity of the results to the value of $\lambda$.
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Transition from weak to strong coupling in thermal gauge theories: Lessons from ${\cal N}=4$ SYM Theory
Padé interpolation between NLO weak- and strong-coupling results places the thermal N=4 SYM transition region at 't Hooft coupling λ roughly between 3 and 14.