Spectra, reconstructions and pole-skipping

<!--HTML--><p>The poles of two-point functions in momentum space, which can be computed and analysed using holographic methods, reveal various details of the physical properties of spectra in QFTs. In thermal QFTs, the lowest-energy (IR) gapless mode is usually described by the theory of hydrodynamics. Assuming a known dispersion relation of only a single hydrodynamic mode, I will discuss when and how the reconstruction of the complete spectrum of physical excitations is possible in the corresponding correlator. In particular, I will demonstrate our recently developed constructive algorithm based on the theorems of Darboux and Puiseux that allows for a reconstruction of all modes connected by `level-crossings’ in the associated spectral curve, from IR to UV. In the second part of my talk, I will introduce the phenomenon of pole-skipping (formally, a “0/0”) in such correlators and discuss how its knowledge can itself be sufficient to reconstruct the entire spectrum.</p>