Holographic Aspects of Chaos and Integrability in String- and M-Theory

In this thesis we investigate classical integrability of the string worldsheet on dierent super-gravity backgrounds. We focus in particular on the class of half-supersymmetric AdS7 solutions of Massive Type IIA supergravity, that are thought to be the near-horizon limit of a D6-D8-NS5 Hanany-Witten brane set-up, and are dual to six-dimensional conformal eld theories with N = (1, 0) supersymmetry. We use both analytical and numerical methods to show the (bosonic sector of the) string worldsheet is non-integrable on most of these backgrounds. The backgrounds on which the string is integrable are an innite massless solution (corresponding to an innite constant quiver), and a background corresponding to an innite linear quiver theory.In addition we nd that the (bosonic sector of the) string is integrable on a background that we call AdS7 × (S3)λ. For this background we show that it corresponds to a 6d SCFT with an innitely long quiver with an innite number of avour groups, all proportional to the colour groups. We study this particular supergravity background in detail, and suggest it corresponds to the large-N limit of the dual SCFT in the limit where the Chern-Simons level k goes to innity.This integrable AdS7 × (S3)λ background can be obtained as the λ-deformation of AdS7×S3. In this context we study integrable deformations of supergravity backgrounds in the last part of this thesis, in particular non-Abelian T-duality. We present another back-ground on which the string is integrable by performing two non-Abelian T-dualities on two three-spheres inside the AdS5×S5 solution and study the resulting background.