Horizon constraints on holographic Green's functions

Understand

We explore a new class of general properties of thermal holographic Green's functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes.

• We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green's functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations.
• From a boundary perspective these `pole-skipping' points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green's function intersects with a line of zeroes.
• As a consequence the dispersion relations of collective modes in the boundary theory at energy scales $\omega\sim T$ are directly constrained by the bulk dynamics near the black-brane horizon.