When a black hole is perturbed — by infalling matter, a merger, or a quantum fluctuation — it rings. The ringing frequencies are quasinormal modes: complex numbers whose real parts give the oscillation frequency and imaginary parts give the decay rate. Computing these frequencies for generic black holes is hard.
This paper maps the problem onto gauge theory. The master equation for scalar perturbations of an extremal Reissner-Nordström black hole (charged, non-rotating, at the limit where the horizon is as small as the mass allows) is equivalent to the quantum Seiberg-Witten curve of N=2 SU(2) supersymmetric gauge theory. The black hole's quasinormal modes become the quantization conditions of the gauge theory.
The mapping is not metaphorical. The differential equation governing perturbations around the black hole is, after a change of variables, the same differential equation that appears in the gauge theory's low-energy effective description. The Seiberg-Witten prepotential — computed exactly using instanton counting and localization — provides a non-perturbative formula for the quasinormal mode frequencies.
The results match numerical computations. At the extremal limit, the spectrum develops quasi-resonances — modes whose imaginary part becomes very small, meaning the black hole rings for a long time before decaying. The gauge theory framework captures this behavior exactly, including the approach to the extremal limit where standard perturbative methods break down.
Two domains of physics — black hole ringdown and supersymmetric gauge theory — share a mathematical skeleton. The black hole's voice is encoded in a gauge theory's vacuum structure.