Black Holes and Chaos

Abstract

We study some aspects of quantum chaos and its relation to scattering near the black hole event horizon, in the context of gauge/gravity dualities. Chaos is an important ingredient related to the onset of thermalization. A signal of chaos is given by the behavior of out-of-time-ordered correlators (OTOC) and exponential growth of commutators. In the gravity side this growth is controlled by a near-horizon high energy scattering, semiclassically described by a shockwave geometry.

A holographic quantum mechanical toy model was developed by Kitaev, the SYK model, consisting of a large number of interacting Majorana fermions without a quasi-particle description. At low temperatures, this system has an emergent conformal symmetry. The thermodynamics and chaos of the model are described by the Schwarzian mode associated to the pattern of breaking of the conformal symmetry, which is also equivalent to the boundary gravitons of dilaton-gravity in 2D. We solve the physics of this mode exactly, including the computation of OTOC. We also study its semiclassical limit and find how the shockwave S-matrix describing near-horizon scattering emerges.

We propose and study a natural extension of the SYK model to two dimensions that presents holographic behavior described by gravity in three dimensions. We also study a natural two-dimensional generalization of the Schwarzian mode, which controls the chaos exponent of the system.

Finally, we study a generalization of the shockwave geometry to include quantum interference effects. This can be used to obtain interesting bounds for general CFTs in higher dimensions.