Pole-skipping of Holographic Correlators: Aspects of Gauge Symmetry and Generalizations

Abstract: In the framework of anti-de Sitter space/conformal field theory (AdS/CFT), we study the pole-skipping phenomenon of the holographic correlators of boundary operators. We explore the locations of the pole-skipping points case by case with the models of $U(1)$-gauged form fields propagating in the asymptotic AdS bulk of finite temperature. In general, in different cases all the first-order points are located at the Matsubara frequency with corresponding wave vectors regularly dispersed in the momentum space. Specifically, in the massless cases with $U(1)$ symmetry, the wave vectors of the pole-skipping points have a form-number dependence, and a trans-mode equivalence in the dual fields is found in correspondence with electromagnetic duality. In the massive cases with explicit symmetry breaking, we find that the appearance of a non-zero mass yields extra pole-skipping points which reduce to the massless results in zero mass limit. We expect in such kind of pole-skipping properties implications of distinctive physics in the chaotic systems. Our near-horizon computation is verified with the double-trace method especially in the example of 2-form where there is dimension-dependent boundary divergence. We illustrate in these cases that the pole-skipping properties of the holographic correlators are determined by the IR physics, consistent with the ordinary cases in previous studies.