Chaos, averaging and holography in LLM geometries

We consider the dynamics of geodesics in Lin-Lunin-Maldacena (LLM) bubbling AdS solutions. The LLM solutions can be characterized by black and white patterns in a plane, which become gray upon ensemble averaging or coarse-graining. We find that the geodesics in black and white geometries exhibit complicated behavior with both chaos and trapping, corresponding to complex structure of the coherent states of long single-trace operators in dual CFT. For short times, this behavior is self-averaging and the average over geodesics is well-approximated by the geodesics in averaged (grayscale) backgrounds; at long times, the self-averaging breaks down completely. We discuss how this might correspond to thermal features of the CFT correlators, and more generally what is the holographic dictionary entry for bulk chaos.”