A weakly non-abelian decay channel

TL;DR

This paper explores non-abelian branes in curved spaces, revealing new decay channels for vacua that are resistant to abelian destabilizations, with implications for the weak gravity conjecture.

Contribution

It introduces solutions for non-abelian branes in AdS flux vacua, showing they can be less self-attractive and enable novel decay pathways.

Findings

Non-abelian branes can be less self-attractive than abelian ones.

Certain non-abelian branes can destabilize vacua resistant to abelian decay.

Embedding these branes in AdS vacua demonstrates new decay channels.

Abstract

We investigate non-abelian branes in curved space. We discuss solutions to the equations of motion of the transverse scalars when they are constant along the world-volume directions and obey an $\mathfrak{su}(2)$ or an $\mathfrak{su}(2)\oplus\mathfrak{su}(2)$ algebra. Motivated by the membrane version of the weak gravity conjecture, we specialise our results to non-abelian domain-wall D$(d-2)$ branes embedded in AdS$_d$ flux vacua. We find that they can be less self-attractive than their abelian counterpart, opening up a new decay-channel for vacua that resist all abelian domain-wall destabilisations. These branes come in two types, depending on whether their fuzziness involves the radial direction, or is purely internal. Only the latter can develop in vacua free from abelian decays. We illustrate our construction by embedding these branes in a variety of AdS vacua, destabilising some of them.