A weakly non-abelian decay channel

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.

💡 Research Summary

This paper investigates the role of non-abelian branes as a novel decay channel for Anti-de Sitter (AdS) flux vacua in string theory, motivated by the membrane version of the Weak Gravity Conjecture (WGC). The central object of study is a stack of N coincident Dp-branes, where the transverse scalar fields become non-commuting matrices in the adjoint representation of U(N). The authors focus on configurations where these scalars are constant along the world-volume and satisfy either an su(2) or an su(2)⊕su(2) algebra.

The primary technical achievement is a general expansion, up to order α’^2, of the Myers effective action for non-abelian branes in a generic curved background with fluxes. This expansion is performed under a gauge condition (E_{ai}=0) and further simplified by assuming constant scalars and a vanishing world-volume gauge field. The resulting action forms the basis for analyzing the dynamics of these “fuzzy” branes.

The core application is to domain-wall D(d-2) branes embedded in AdS_d flux vacua. According to the WGC, a decay channel opens if there exists a brane whose tension (T) is less than its charge (Q). The paper computes how non-abelian corrections modify the tension of such a brane. While the charge remains identical to that of a single abelian brane (confirming its dielectric nature), the tension receives corrections from terms like