Constrained Padé Ensembles for Thermal N=4 SYM: Quantified Uncertainties and Next-Order Predictions (2510.22583v1)

Abstract: We quantify the transition between weak and strong coupling in thermal $\mathcal N=4$ supersymmetric Yang-Mills (SYM) theory in four space-time dimensions by constructing an \emph{admissible ensemble} of log-aware Pad\'e approximants that exactly reproduce the weak- and strong-coupling expansions through $\mathcal O(\lambda^2)$ and $\mathcal O(\lambda^{-3/2})$ (where $\lambda$ is the 't Hooft coupling), including the nonanalytic $\lambda^{3/2}$ and $\lambda^{2}\log\lambda$ terms. This replaces single-curve estimates with a reproducible uncertainty band and a well-defined central curve across the intermediate regime. Applying the same construction to transport, the $\eta/s$ band connects perturbative behavior to the Kovtun-Son-Starinets limit. The framework is \emph{predictive}, yielding $A_{5/2}=0.476\pm0.095$ on the weak side and a model-independent bound on the next strong-coupling term, thereby setting testable benchmarks for forthcoming perturbative and holographic calculations.