Establish the higher-genus Okuda–Penedones limit

Establish the existence of the Okuda–Penedones limit for perturbative string amplitudes in \(AdS_5\times S^5\) at higher orders in the string-coupling expansion, including the effects of Kaluza–Klein modes propagating in loop diagrams, in particular at order \(O(g_s)\).

Background

The analysis in the paper is restricted to tree-level amplitudes. At loop level, even when external states carry zero momentum along S5S^5, nontrivial Kaluza–Klein modes can propagate internally, making the direct extension of the construction substantially more complicated.

A higher-genus extension is needed to determine whether the doubly scaled SYM sector genuinely defines a Carrollian theory with a genus expansion and to clarify whether the putative dual remains four-dimensional or develops an emergent higher-dimensional structure. The authors identify proving the existence of the limit at order O(gs)O(g_s) as an essential step.

References

The extension of the OP limit to perturbative string amplitudes in AdS_{5}\, \times\, S{5} at higher order in g_{s} expansion remains completely open as the KK modes in S{5} will propagate along the loops even if the external kinematics was supported only in {\mathbb{R}{1,3}. To ensure that the Carrollian correlators we have obtained exist as correlation functions of a theory which admits a genus expansion, proof of the existence of an OP limit at O(g_{s}) appears essential.

— Doubly-scaled planar ${\cal N} = 4$ SYM \& Carroll Holography  (2608.27410 - Bagchi et al., 27 Aug 2026) in Section “Conclusion,” paragraph following the graviton-amplitude open problem