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.