Duality Constraints on Thermal Spectra of 3D Conformal Field Theories and 4D Quasinormal Modes

Thermal spectra of correlation functions in holographic 3D large-N conformal field theories (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 and relates infinite products over QNMs with 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.