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Pole-skipping with finite-coupling corrections

Recently, it is shown that many Green's functions are not unique at special points in complex momentum space using AdS/CFT. This phenomenon is similar to the pole-skipping in holographic chaos, and the special points are typically located at $ω_n = -(2πT)ni$ with appropriate values of complex wave number $q_n$. We study finite-coupling corrections to special points. As examples, we consider four-derivative corrections to gravitational perturbations and four-dimensional Maxwell perturbations. While $ω_n$ is uncorrected, $q_n$ is corrected at finite coupling. Some special points disappear at particular values of higher-derivative couplings. Special point locations of the Maxwell scalar and vector modes are related to each other by the electromagnetic duality.