Description
The quantum Seiberg–Witten (SW) curve approach to the black hole (BH) perturbation theory problem provides a solid framework for obtaining analytical results. The Coulomb branch moduli space of the SW theory is topologically a torus and is therefore characterized by two cycles. In the quantum theory, these cycles enter the exact Born–Sommerfeld like quantization condition for quasi-normal modes (QNMs). After a brief theoretical overview of the N=2 SU(2) SYM theory, I will show how to apply this framework to compute the QNMs of Reissner–Nordström BHs with effective-field-theory corrections. The main result is that the causality requirement of the gravitational theory, formulated at the level of QNMs, translates into the same constraint on EFT couplings that appears in the Weak Gravity Conjecture. Furthermore, using a geodesic analogy, I will discuss certain resummation properties of the SW cycles in the Post-Minkowskian regime.