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

Abstract

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 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.

7 pages, 1 figure, v3: minor corrections, added appendix

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Cited by in corpus (4)

• Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
• The Algebraic Structure Underlying Pole-Skipping Points
• Bulk Spacetime Encoding via Boundary Ambiguities
• Thermal Product Formula for Shear Modes