Heavy AdS‑state contribution in the flat‑space limit

Prove from first principles that the heavy (AdS) states’ contribution to the fixed‑t dispersion relation for the Coulomb‑branch four‑point amplitude admits a well‑defined polynomial (moment) expansion in the flat‑space scaling variables (S,T) as g→∞, or determine the precise conditions under which this non‑enhancement and polynomial behavior hold.

Background

In separating flat‑space states from heavy AdS states in the dispersion relation, the authors assume the latter yield a polynomial in the flat‑space kinematic variables after appropriate scaling.

They note this requires certain moments not to be enhanced at large coupling g, an assumption they cannot currently derive. Establishing or disproving this would clarify the validity of the flat‑space low‑energy expansion with AdS contributions.