Classifying integrable symmetric space strings via factorized scattering

TL;DR

This paper classifies integrable symmetric space string solutions in type II supergravity, confirming integrability for supersymmetric cases and ruling it out for non-supersymmetric solutions through scattering analysis.

Contribution

It completes the classification of symmetric space strings by demonstrating non-integrability of non-supersymmetric solutions via worldsheet scattering.

Findings

Supersymmetric solutions are classically integrable.

Non-supersymmetric solutions are not integrable, as shown by scattering analysis.

Tree-level scattering fails to factorize in non-supersymmetric cases.

Abstract

All symmetric space $AdS_n$ solutions of type II supergravity have recently been found for $n>2$. For the supersymmetric solutions (and their T-duals) it is known that the Green-Schwarz string is classically integrable. We complete the classification by ruling out integrability for the remaining non-supersymmetric solutions. This is achieved by showing that tree-level scattering on the worldsheet of a GKP or BMN string fails to factorize for these cases.