Black Hole Monodromy and Conformal Field Theory

TL;DR

This work establishes a monodromy-based approach to black hole scattering, showing that the global analytic structure of the Klein–Gordon equation in Kerr geometry encodes both black hole thermodynamics and hidden conformal symmetry. By treating the radial equation as a flat SL(2;ℂ) connection with three singular points, the authors derive monodromy matrices whose products equal unity and express transmission (greybody) factors purely in terms of monodromy data, revealing how inner-horizon information influences observables. They reinterpret the monodromy basis as defining local vacuum states and demonstrate that, in the appropriate basis, low-energy scattering matches a two-dimensional CFT with left and right sectors characterized by temperatures T_L and T_R and energies ω_L, ω_R, with α_irr encoding conformal weight. The framework generalizes to other three-singular-point black holes (e.g., Myers–Perry, Kerr–AdS), suggesting a universal hidden conformal symmetry class and linking thermodynamic Noether charges to monodromy data. Altogether, the paper provides a non-perturbative, geometry-based bridge between black hole thermodynamics and CFT descriptions, with implications for understanding microstates and Hawking spectra.

Abstract

The analytic structure of solutions to the Klein-Gordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the "hidden conformal symmetry" of a non-extremal black hole, and it explains why features of the inner event horizon appear in scattering data such as greybody factors. This indicates that hidden conformal symmetry is generic within a universality class of black holes.