Probing analytical and numerical integrability: the curious case of (AdS5 \xd7 S5)\u03b7

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.