My talk will present two recently uncovered connections between hydrodynamics and many-body chaos—one at strong and one at weak coupling. I will begin by introducing some relevant concepts from the field of relativistic hydrodynamics, which will be followed by a short discussion of holographic duality. In particular, I will describe how thermal field theory correlation functions can be inferred from the properties of black holes. I will then show how in strongly interacting theories with simple holographic duals both the Lyapunov exponent and the butterfly velocity can be computed from a retarded longitudinal energy-energy two-point function, without the need for computing the OTOC. This makes the connection between holographic many-body chaos and hydrodynamics precise. Finally, by constructing a modified kinetic, Boltzmann-like equation, both phenomenologically and from an OTOC, I will argue that even at weak coupling, hydrodynamic and chaotic properties can be intimately related.

* Sašo Grozdanov, MIT – Center for Theoretical Physics