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

TL;DR

This paper applies the Exact WKB analysis to study quasi-normal modes of D3-branes, providing exact conditions, numerical verification, and analytic expressions for the QNMs in this context.

Contribution

It introduces the use of Exact WKB analysis for D3-brane QNMs, offering exact conditions and asymptotic behaviors, which is a novel approach in this area.

Findings

Exact condition for D3-brane QNMs derived

Numerical verification using Borel-Padé approximation

Analytic and asymptotic forms of QNMs provided

Abstract

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-Pad\'{e} approximation. We also present an analytic form and an asymptotic behavior of the QNMs.