The second-order quasi-normal modes for AdS black branes

TL;DR

This paper develops a gauge-invariant method to analyze second-order quasi-normal modes in AdS black branes, revealing resonant divergences linked to three-point correlators in the dual quantum field theory, thus connecting gravitational nonlinearities with quantum observables.

Contribution

It introduces a novel gauge-invariant framework for second-order gravitational perturbations in AdS black branes and links resonant divergences to boundary quantum correlators.

Findings

Resonant divergences occur when source mode frequencies sum to a third mode's frequency.

Divergences manifest as poles in three-point energy-momentum tensor correlators.

The work deepens the holographic understanding of nonlinearities in quantum many-body systems.

Abstract

We investigate second-order gravitational perturbations in asymptotically AdS black branes, developing a gauge-invariant framework to compute the amplitude ratio between quadratic and linear quasi-normal modes. Our analysis reveals resonant divergences of this ratio when the summed frequencies of two source modes coincide with the frequency of a third mode. These divergences are shown to manifest as poles in three-point fully retarded correlators of the energy-momentum tensor in the holographically dual quantum field theory, establishing a concrete connection between bulk gravitational nonlinearities and observables in the dual boundary theory. Our findings contribute to the understanding of nonlinearity in quantum many-body systems while deepening the holographic dictionary between spacetime dynamics and quantum correlations.