Systematic structure of the strong‑coupling expansion

Determine the systematic structure of the strong‑coupling (large‑g) expansion of the rescaled four‑point amplitude \hat f(S,T) in scattering on the Coulomb branch of planar N=4 SYM, including whether non‑analytic terms such as log g appear and how to organize the expansion consistently beyond the leading 1/g correction.

Background

The authors construct the first 1/g correction to the super‑Veneziano amplitude using a worldsheet ansatz constrained by symmetries and spectrum, but they emphasize that the global structure of the strong‑coupling series is unknown.

Clarifying whether non‑analytic terms (e.g., involving log g) occur is important for establishing a controlled asymptotic expansion and for matching to weak‑coupling behaviors where logarithms are known to arise.