Constraints on quasinormal modes and bounds for critical points from pole-skipping

Abstract

We consider a holographic thermal state and perturb it by a scalar operator whose associated real-time Green’s function has only gapped poles. These gapped poles correspond to the non-hydrodynamic quasinormal modes of a massive scalar perturbation around a Schwarzschild black brane. Relations between pole-skipping points, critical points and quasinormal modes in general emerge when the mass of the scalar and hence the dual operator dimension is varied. First, this novel analysis reveals a relation between the location of a mode in the infinite tower of quasinormal modes and the number of pole-skipping points constraining its dispersion relation at imaginary momenta. Second, for the first time, we consider the radii of convergence of the derivative expansions about the gapped quasinormal modes. These convergence radii turn out to be bounded from above by the set of all pole-skipping points. Furthermore, a transition between two distinct classes of critical points occurs at a particular value for the conformal dimension, implying close relations between critical points and pole-skipping points in one of those two classes. We show numerically that all of our results are also true for gapped modes of vector and tensor operators.

Chaos and pole-skipping in rotating black holes

“…In this paper, our goal is to study the relationship between many-body quantum chaos and energy dynamics for an example dual to a higher-dimensional rotating black hole, 1 In addition to the above example, holographic theories also exhibit pole-skipping in the lower-half plane of complex frequency space [22]. These are not directly connected to the form (1.1) of the OTOC, but can still provide interesting constraints on the dispersion relations of the field theory's collective excitations [23][24][25][26][27][28][29][30][31][32][33][34][35].…”

A holographic superfluid symphony

“…dynamics throughout the phase diagram following the recent studies [50,[108][109][110][111][112][113][114][115][116][117][118][119] in other holographic models.…”

Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

“…However, unlike the energy density two point function, the pole-skipping in other cases turned out not to be related to chaos. See also recent developments of pole-skipping in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”