Chaotic Behavior of Perturbed Conformal Field Theories

Chaos in quantum systems has historically been challenging to quantify. One measure of the strength of chaos is the Lyaponov exponent λ_L. Previously, λ_L has been found for certain quantum field theories by analyzing out-of-time ordered four point functions. While this procedure is helpful for certain systems, performing this computation is generically quite challenging. Recently, progress has been made in extracting λ_L from the two-point function of the energy density operator. Specifically, one determines the exponent by finding special points where poles are skipped (where a zero in the denominator is balanced by one in the numerator). This procedure has been fruitful in holographic (gauge/gravity duality) systems as well as in SYK models. In this work, we start by considering two-dimensional conformal field theories. We then perturb away from the conformal point and analyze what happens to this pole-skipping phenomena. In this way, we track how the chaotic behavior of the system changes after a perturbation to a more general class of theories.