  We study three prominent diagnostics of chaos and scrambling in the context
of two-dimensional conformal field theory: the spectral form factor,
out-of-time-ordered correlators, and unitary operator entanglement. With the
observation that all three quantities may be obtained by different analytic
continuations of the torus partition function, we address the connections and
distinctions between the information that each quantity provides us. In this
process, we study the emergence of irrationality from "large-N" limits of
rational conformal field theories (RCFTs) as well as the explicit breakdown of
rationality for theories with central charges greater than the number of their
conserved currents. Our analysis begins to elucidate the intermediate dynamical
behavior of theories that bridge the gap between integrable RCFTs and maximally
chaotic holographic CFTs.

High Energy Physics - Theory;Statistical Mechanics;Strongly Correlated Electrons