Bootstrap AdS Veneziano Amplitude with Arbitrary Kaluza-Klein Modes

TL;DR

This work derives the first curvature correction to the open-string AdS Veneziano amplitude for arbitrary KK modes using a world-sheet bootstrap tied to the AdS×S Mellin formalism. By matching residues from the conformal-block expansion to a finite, single-valued polylogarithm-based world-sheet ansatz, they obtain a unique $\mathcal{A}^{(1)}$ independent of low-lying KK data and extract new low-energy Wilson coefficients. The analysis reveals a universal high-energy exponent for AdS stringy amplitudes, exhibiting a precise relation between open and closed string limits, and provides a coherent framework linking KK structure to both the low-energy EFT and high-energy Regge-like behavior. Methodologically, the approach unifies KK dependence via AdS×S Mellin variables and SVMPLs, with potential extensions to higher curvature orders, closed-string sectors, and non-planar corrections. The results corroborate localization and integrability insights and offer explicit predictions for averaged OPE data across KK towers.

Abstract

We present a derivation of the first curvature correction to the AdS Veneziano amplitude for arbitrary Kaluza-Klein (KK) modes, using a bootstrap approach based on the world-sheet representation and AdS$\times$S formalism. Our results establish a universal formula for the first order curvature correction without considering any low-lying KK configurations. We give new predictions for Wilson coefficients in the low-energy expansion. In the high-energy regime, the amplitude exhibits a universal exponent independent of the external KK charges, providing a coherent picture of AdS stringy amplitudes in different backgrounds.