  Thermal spectra of correlation functions in holographic 3d large-N CFTs
correspond to quasinormal modes of classical gravity and other fields in
asymptotically anti-de Sitter black hole spacetimes. Using general properties
of such spectra along with constraints imposed by the S-duality (or the
particle-vortex duality), we derive a spectral duality relation that all such
spectra must obey. Its form is universal in that each such relation (expressed
as an infinite product over QNMs) only depends on a single function of a
spatial wavevector that corresponds to the bulk algebraically special
frequencies. In the process, we also derive a new sum rule constraining
products over QNMs. The spectral duality relation, which imposes an infinite
set of constraints on the QNMs, is then investigated and a number of well-known
holographic examples that demonstrate its validity are examined. Our results
also allow us to understand several new aspects of the pole-skipping
phenomenon.
