Dynamical tidal response of regular black holes: perturbative analysis and shell EFT interpretation

We investigate the frequency-dependent (dynamical) tidal response of regular black holes for the Bardeen, Hayward, and Fan-Wang geometries. Our results are obtained by solving the coupled perturbation equations with appropriate boundary conditions, together with a `shell effective field theory' (EFT) construction in which the tidal response is encoded in renormalized, frequency-dependent response functions. In the polar sector, the frequency-dependent Love numbers exhibit strong dispersion, including oscillatory and resonant features, while smoothly recovering the static results in the zero-frequency limit. In the axial sector, where gravitational and electromagnetic perturbations remain coupled, the response shows a simpler but strongly frequency-dependent enhancement near extremality. The shell EFT analysis provides a gauge-invariant effective description of the tidal response and clarifies its renormalization structure, including the separation of scheme-independent logarithmic running and scheme-dependent finite contributions to the response coefficients, with the corresponding Wilson coefficients determined by matching to the black hole perturbation theory. Our results establish dynamical tidal Love numbers as well-defined EFT observables for regular black holes and show that they encode information about near-horizon and interior structure that is not accessible in the static limit.