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

TL;DR

This paper derives universal duality relations for the thermal spectra of 3d holographic CFTs, linking quasinormal modes to S-duality constraints, and explores implications for pole-skipping phenomena.

Contribution

It introduces a universal spectral duality relation for QNMs in holographic CFTs based on S-duality, and derives a new sum rule constraining QNM products.

Findings

Validated duality relations with known holographic examples.

Derived a new sum rule for quasinormal mode products.

Enhanced understanding of pole-skipping phenomena in holography.

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.