Pole Skipping in Holographic Theories with Bosonic Fields

We study pole skipping in holographic conformal field theories dual to diffeomorphism invariant theories containing an arbitrary number of bosonic fields in the large N limit. Defining a weight to organize the bulk equations of motion, a set of general pole skipping conditions are derived. In particular, the frequencies simply follow from general covariance and weight matching. In the presence of higher-spin fields, we find that the imaginary frequency for the highest-weight pole skipping point equals the higher-spin Lyapunov exponent which lies outside of the chaos bound. Without higher-spin fields, we show that the energy density Green's function has its highest-weight pole skipping happening at a location related to the out-of-time-order correlator for arbitrary higher-derivative gravity, with a Lyapunov exponent saturating the chaos bound and a butterfly velocity matching that extracted from a shockwave calculation. We also suggest an explanation for this matching at the metric level by obtaining the on-shell shockwave solution from a regularized limit of the metric perturbation at the skipped pole.