Chaotic string dynamics from perturbation theory to matrix models

We explore the chaotic properties of string motion and relate them to operator growth and complexity in dual field theories. The nonperturbative regime can be studied in the framework of the IKKT (type IIB) matrix model, where we compute the time-ordered and out-of-time-ordered correlator (TOC and OTOC) and show that both have a complex structure: there is no factorization of TOC at long times and chaos is weak, with no universal bounds or properties. On the other hand, the perturbative semiclassical regime for a falling string in AdS black brane background (corresponding to jets in dual super Yang Mills theory) saturates the universal chaos bound in the bulk but not in dual gauge theory. We conclude that chaos in string motion is directly related not to OTOC but to more refined measures of complexity in dual field theory.