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

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.

arXiv comment17 pages, Published version

References in corpus (20)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Quasinormal modes of black holes: from astrophysics to string theory
• Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach
• Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
• Quasinormal modes of black holes. The improved semianalytic approach
• Instantons and recursion relations in N=2 Susy gauge theory
• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Quasi-normal modes of charged, dilaton black holes
• QNMs of branes, BHs and fuzzballs from Quantum SW geometries
• Quasinormal modes of weakly charged Einstein-Maxwell-dilaton black holes
• Quasinormal Modes of Dilaton Black Holes: Analytic approximations
• Bernstein spectral method for quasinormal modes of a generic black hole spacetime and application to instability of dilaton-de Sitter solution
• Quasinormal Modes of C-metric from SCFTs
• Quasi-normal modes for the D3-branes and Exact WKB analysis
• Exact conditions for Quasi-normal modes of extremal M5-branes and Exact WKB analysis
• Duality between Seiberg-Witten Theory and Black Hole Superradiance
• Kerr-Newman quasinormal modes and Seiberg-Witten theory
• Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory