More on the SW-QNM correspondence

TL;DR

This paper leverages a gauge/gravity correspondence to compute black hole quasi-normal modes using quantum Seiberg-Witten curves, demonstrating strong agreement with numerical and approximation methods, and explores implications for black hole physics.

Contribution

It introduces a novel approach connecting gravitational perturbations to quantum gauge theories, providing analytical tools and insights into black hole spectra and their physical properties.

Findings

QNM frequencies match numerical and WKB results

Analytic solutions for toy-models illustrate the method

Insights into black hole properties like tidal Love numbers

Abstract

We exploit the recently proposed correspondence between gravitational perturbations and quantum Seiberg-Witten curves to compute the spectrum of quasi-normal modes of asymptotically flat Kerr Newman black holes and establish detailed gauge/gravity dictionaries for a large class of black holes, D-branes and fuzzballs in diverse dimensions. QNM frequencies obtained from the quantum periods of $SU(2)$ ${\cal N}=2$ SYM with $N_f=3$ flavours are compared against numerical results, WKB (eikonal) approximation and geodetic motion showing remarkable agreement. Starting from the master example relating quasi-normal modes of Kerr-Newman black holes in AdS$_4$ to $SU(2)$ gauge theory with $N_f=4$, we illustrate the procedure for some simple toy-models that allow analytic solutions. We also argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/Seiberg-Witten connection and further elucidate interesting properties (such as tidal Love numbers and grey-body factors) that can help discriminating black holes from fuzzballs.