Exact conditions for Quasi-normal modes of extremal M5-branes and Exact WKB analysis

TL;DR

This paper derives exact conditions for quasi-normal modes of extremal M5-branes using WKB analysis, revealing how perturbative discontinuities influence non-perturbative modes and illustrating a Seiberg-Witten/gravity correspondence.

Contribution

It introduces exact QNM conditions for extremal M5-branes via WKB analysis and demonstrates their relation to non-perturbative effects and Seiberg-Witten/gravity correspondence.

Findings

Exact QNM conditions depend on the argument of complex frequency.

Discontinuities in perturbative parts influence non-perturbative modes.

A new Seiberg-Witten/gravity correspondence example is presented.

Abstract

We study the quasi-normal modes (QNMs) of a massless scalar perturbation to the extremal M5-branes metric by using the exact WKB analysis. The exact WKB analysis provides two exact QNMs conditions depending on the argument of the complex frequency of the perturbation. The exact conditions show that the discontinuity of the perturbative part of the QNMs leads the non-perturbative part of themselves. We also find a new example of the Seiberg-Witten/gravity correspondence, which helps us to compute the QNMs from our conditions.