Reconstruction of the quasinormal spectrum from pole-skipping

Abstract: The holographic gauge/gravity duality provides an explicit reduction of quantum field theory (QFT) calculations in the semi-classical large-$N$ limit to sets of `gravitational' differential equations whose analysis can reveal all details of the spectra of thermal QFT correlators. We argue that in certain cases, a complete reconstruction of the spectrum and of the corresponding correlator is possible from only the knowledge of an infinite, discrete set of pole-skipping points traversed by a single (hydrodynamic) mode computed in a series expansion in an inverse number of spacetime dimensions. Conceptually, this reduces the computation of a QFT correlator spectrum to performing a set of purely algebraic manipulations. With the help of the pole-skipping analysis, we also uncover a novel structure underpinning the coefficients that enter the hydrodynamic dispersion relations.