Probing analytical and numerical integrability: the curious case of (AdS5 × S5)η

Abstract

Motivated by recent studies related to integrability of string motion in various backgrounds via analytical and numerical procedures, we discuss these procedures for a well known integrable string background (AdS5 × S5)η. We start by revisiting conclusions from earlier studies on string motion in (ℝ × S3)η and (AdS3)η and then move on to more complex problems of (ℝ × S5)η and (AdS5)η. Discussing both analytically and numerically, we deduce that while (AdS5)η strings do not encounter any irregular trajectories, string motion in the deformed five-sphere can indeed, quite surprisingly, run into chaotic trajectories. We discuss the implications of these results both on the procedures used and the background itself.