The stability of the shell of D6-D2 branes in a ${\cal N}=2$ supergravity solution

TL;DR

This paper investigates the stability of D6-brane shells wrapped on K3 in supergravity, showing that supersymmetric solutions are stable at any radius, but resonances occur below the enhançon radius indicating a classical instability.

Contribution

It provides a detailed supergravity analysis of shell stability, including effective energy-momentum tensor construction and perturbation analysis, revealing stability conditions and resonance phenomena.

Findings

Supersymmetric solutions satisfy Israel's junction conditions at any radius.

No imaginary eigenmodes found, indicating classical stability.

Resonances occur when the shell radius is below the enhançon radius.

Abstract

The stability of the shell of wrapped D6-branes on K3 is investigated from the point of view of supergravity. We first construct an effective energy-momentum tensor for the shell under the reasonable conditions and show that supersymmetric solutions satisfy Israel's junction conditions at arbitrary radius of the shell. Next we study the perturbation of the whole system including the self-gravity of the shell. It is found that in spite of the existence of wrapped D6-branes with negative tension, there is no eigenmode whose frequencies of the shell and the fields are imaginary numbers, at any radius of the shell. Furthermore, when the radius of the shell is less than the enhan\c{c}on radius, resonances are produced, and this indicates a kind of ``instability'' of the system. This can even classically explain why the shell is constructed at the enhan\c{c}on radius.