Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3

TL;DR

This paper develops Y-systems for form factors in N=4 SYM at strong coupling, extending previous AdS3 results to AdS5 and multi-operator insertions, with implications for QCD amplitudes and correlation functions.

Contribution

It generalizes Y-system constructions to AdS5 and multi-operator cases, linking form factors to spacetime cross ratios and WKB approximations in a strong coupling framework.

Findings

Constructed Y-systems for AdS5 and multi-operator insertions.

Related Y-functions to spacetime cross ratios.

Analyzed WKB approximations using rational functions.

Abstract

We study form factors in N=4 SYM at strong coupling in general kinematics and with multi-operator insertions by using gauge/string duality and integrability techniques. This generalizes the AdS3 results of Maldacena and Zhiboedov in two non-trivial aspects. The first generalization to AdS5 space was motivated by its potential connection to strong coupling Higgs-to-three-gluons amplitudes in QCD which was observed recently at weak coupling. The second generalization to multi-operator insertions was motivated as a step towards applying on-shell techniques to compute correlation functions at strong coupling. In this picture, each operator is associated to a monodromy condition on the cusp solutions. We construct Y-systems for both cases. The Y-functions are related to the spacetime (cross) ratios. Their WKB approximations based on a rational function P(z) are also studied. We focus on the short operators, while the prescription is hopefully also applicable for more general operators.