The non-SUSY $AdS_6$ and $AdS_7$ fixed points are brane-jet unstable

In six- and seven-dimensional gauged supergravity, each scalar potential has one supersymmetric and one non-supersymmetric fixed points. The non-supersymmetric $AdS_7$ fixed point is perturbatively unstable. On the other hand, the non-supersymmetric $AdS_6$ fixed point is known to be perturbatively stable. In this note we examine the newly proposed non-perturbative decay channel, called brane-jet instabilities of the $AdS_6$ and $AdS_7$ vacua. We find that when they are uplifted to massive type IIA and eleven-dimensional supergravity, respectively, the non-supersymmetric $AdS_6$ and $AdS_7$ vacua are both brane-jet unstable, in fond of the weak gravity conjecture.