Loop corrections for Kaluza-Klein AdS amplitudes

TL;DR

This work extends the one-loop AdS${}_5\times S^5$ amplitude to include KK modes, solving a nontrivial operator-mixing problem in the $[0,1,0]$ sector to obtain explicit leading anomalous dimensions and OPE data. By computing double discontinuities from the OPE and uplifting them with ladder integrals and single-valued polylogarithms, the authors derive a full one-loop correlator for mixed graviton/Kaluza-Klein external states and extract twist-5 anomalous dimensions. A robust symmetry maps data across spin families, linking even/odd sectors and offering a Casimir-based organizing principle that persists to one loop. The results provide a concrete, cross-checked framework for loop corrections in AdS/CFT with KK towers, and establish techniques that can be applied to other KK-reduced sectors and higher-loop analyses.

Abstract

Recently we conjectured the four-point amplitude of graviton multiplets in ${\rm AdS}_5 \times {\rm S}^5$ at one loop by exploiting the operator product expansion of $\mathcal{N}=4$ super Yang-Mills theory. Here we give the first extension of those results to include Kaluza-Klein modes, obtaining the amplitude for two graviton multiplets and two states of the first KK mode. Our method again relies on resolving the large N degeneracy among a family of long double-trace operators, for which we obtain explicit formulas for the leading anomalous dimensions. Having constructed the one-loop amplitude we are able to obtain a formula for the one-loop corrections to the anomalous dimensions of all twist five double-trace operators.