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arXiv · 2406.19790

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

Sašo Grozdanov·Mile Vrbica
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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.

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Sašo Grozdanov, Mile Vrbica. 2024-06-28. Duality Constraints on Thermal Spectra of 3d Conformal Field Theories and 4d Quasinormal Modes. https://doi.org/10.1103/physrevlett.133.211601

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