# Constraining integrable AdS/CFT with factorized scattering

## TL;DR

This paper investigates how integrability constraints on the worldsheet S-matrix restrict the geometry of certain AdS string backgrounds, ruling out integrability in many supersymmetric cases.

## Contribution

It derives constraints on warp factors from integrability, showing that many supersymmetric AdS backgrounds are non-integrable due to these restrictions.

## Key findings

- Integrability constrains warp factors in AdS backgrounds.
- Many supersymmetric AdS backgrounds are incompatible with integrability.
- The results exclude integrability for several classes of AdS solutions.

## Abstract

We consider (warped) AdS string backgrounds which allow for a GKP spinning string/null cusp solution. Integrability implies that the worldsheet S-matrix should factorize, which in turn constrains the form of the warp factor as a function of the coordinates of the internal space. This constraint is argued to rule out integrability for all supersymmetric AdS7 and AdS6 backgrounds as well as AdS5 Gaiotto-Maldacena backgrounds and a few highly supersymmetric AdS4 and AdS3 backgrounds.