Analytic Non-integrability in String Theory

TL;DR

This paper demonstrates that certain classical string configurations in AdS_5 x X_5 backgrounds are non-integrable, indicating complex, non-solvable dynamics in these string theory models.

Contribution

It applies analytic Hamiltonian techniques to establish non-integrability of strings in a broad class of Einstein space backgrounds.

Findings

String configurations in AdS_5 x X_5 are non-integrable.

The non-integrability applies to a large class of Einstein spaces.

The results negatively answer the question of integrability in these backgrounds.

Abstract

Using analytic techniques developed for Hamiltonian dynamical systems we show that a certain classical string configurations in AdS_5 x X_5 with X_5 in a large class of Einstein spaces, is non-integrable. This answers the question of integrability of string on such backgrounds in the negative. We consider a string localized in the center of AdS_5 that winds around two circles in the manifold X_5.