Analytic Computation of Dilaton Black Hole Quasinormal Modes via Seiberg-Witten Theory

TL;DR

This paper introduces a novel approach to compute dilaton black hole quasinormal modes using Seiberg-Witten theory, achieving high accuracy and revealing deep connections between gauge theories and gravity.

Contribution

It develops a gauge-theoretic method to analytically determine black hole quasinormal modes via the quantum Seiberg-Witten curve, bridging supersymmetric gauge theories and gravitational physics.

Findings

QNM frequencies agree with WKB and continued fraction methods within 10^{-3}

Increasing charge or scalar mass raises oscillation frequency

Higher angular momentum reduces damping rate

Abstract

We study the quasinormal modes (QNMs) of dilaton black holes in Einstein-Maxwell-dilaton gravity through a correspondence with the quantum Seiberg-Witten (SW) curve of $\mathcal{N}=2$ SU(2) gauge theory with $N_f=3$ hypermultiplets. By mapping both the black hole perturbation equation and the quantum SW curve to the confluent Heun form, the QNM problem is reformulated in a gauge-theoretic framework, and the spectrum is obtained via the SW quantization condition. The resulting frequencies show excellent agreement with those computed using the WKB and continued fraction methods, with typical deviations below $10^{-3}$. The QNM spectrum exhibits consistent trends: increasing the black hole charge or scalar field mass raises the oscillation frequency, while higher angular momentum reduces the damping rate. These results demonstrate the precision of the quantum SW framework in describing black hole perturbations and reveal new links between supersymmetric gauge theories and gravitational dynamics.