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We present a novel study of Kerr Compton amplitudes in a partial wave basisin terms of the Nekrasov-Shatashvili (NS) function of the \textit{confluentHeun equation} (CHE). Remarkably, NS-functions enjoy analytic properties andsymmetries that are naturally inherited by the Compton amplitudes. Based onthis, we characterize the analytic dependence of the Compton phase-shift in theKerr spin parameter and provide a direct comparison to the standardpost-Minkowskian (PM) perturbative approach within General Relativity (GR). Wealso analyze the universal large frequency behavior of the relevantcharacteristic exponent of the CHE -- also known as the renormalized angularmomentum -- and find agreement with numerical computations. Moreover, wediscuss the analytic continuation in the harmonics quantum number $\ell$ of thepartial wave, and show that the limit to the physical integer values commuteswith the PM expansion of the observables. Finally, we obtain the contributionsto the tree level, point-particle, gravitational Compton amplitude in acovariant basis through $\mathcal{O}(a_{\text{BH}}^8)$, without the need totake the super-extremal limit for Kerr spin.

Black Hole Perturbation Theory Meets CFT$_2$: Kerr Compton Amplitudes from Nekrasov-Shatashvili Functions