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arXiv · 2604.16109

Constrained Pad\'e Ensembles for Thermal $\mathcal{N}{=}4$ SYM with the Exact $\mathcal O(\lambda^{5/2})$ Coefficient

Ubaid Tantary·Qianqian Du
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Abstract

We revisit the constrained log-subtracted two-point Pad\'e (LSTP) ensemble for thermal $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) thermodynamics in four spacetime dimensions after upgrading the weak-coupling truncation from $\mathcal{O}(\lambda^2)$ to the exact $\mathcal{O}(\lambda^{5/2})$ coefficient. We keep the LSTP interpolation ansatz unchanged and shift the weak-side matching points to the regime where the new term is numerically significant. Within the same parameter scan the admissible set collapses from $9$ nominal survivors ($3$ distinct curves) to a single distinct curve, the crossover range shrinks to a unique value, and the pointwise band width drops to zero within numerical resolution. The Hermite-Pad\'e (HP) central curve does not coincide with the unique LSTP survivor, so the updated weak-side matching removes the LSTP scan uncertainty but not the difference between the two routes. The minimal HP extension that also carries the exact coefficient is uniquely determined and develops a spurious pole-zero pair at small coupling. Away from that pair the HP and LSTP curves still differ, so this difference persists at the same weak-coupling order.

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Ubaid Tantary, Qianqian Du. 2026-04-17. Constrained Pad\'e Ensembles for Thermal $\mathcal{N}{=}4$ SYM with the Exact $\mathcal O(\lambda^{5/2})$ Coefficient. https://arxiv.org/abs/2604.16109

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