Quasi-normal modes for the D3-branes and Exact WKB analysis

We demonstrate how the Exact WKB analysis works in the study of the quasi-normal modes (QNMs). We apply the Exact WKB analysis to a massless scalar perturbation to the D3-brane metric as a concrete example. The Exact WKB analysis provides an exact condition for the QNMs. We numerically check our exact condition by using the Borel-Padé approximation. We also present an analytic form and an asymptotic behavior of the QNMs.