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A weakly non-abelian decay channel

Vincent Menet, Alessandro Tomasiello

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.

A weakly non-abelian decay channel

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 or an algebra. Motivated by the membrane version of the weak gravity conjecture, we specialise our results to non-abelian domain-wall D branes embedded in AdS 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.

Paper Structure

This paper contains 30 sections, 90 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Non-abelian branes and flux vacua
  3. Myers' action
  4. General expansion of the Myers action
  5. Constant transverse scalars
  6. A simple solution
  7. The su(2) branes
  8. The su(2)+su(2) branes
  9. $\mathfrak{su}(3)$ branes
  10. Purely domain-wall branes
  11. Domain-wall instability
  12. Internal fuzziness
  13. The su(2) branes
  14. Consequences for supersymmetric vacua
  15. The su(2)+su(2) branes
  16. ...and 15 more sections

Figures (2)

  • Figure 1: The $f_6$ flux for various $\mathbb{CP}^3$ vacua. The red branches correspond to the vacua destabilised by abelian domain-wall D2 branes. The solutions in black are stable against the nucleation of these branes.
  • Figure 2: $B_{r}$ as a function of $f_3$ and $f_4$. The black region corresponds to $f_1<3$, where the abelian D2 doesn't destabilise the vacua. No non-abelian branes can sit at a stationary point of the abelian potential in this region, so our solutions don't exist. $B_{r}$ is red where the abelian D2 is superextremal and thus destabilises the vacua, but the bound \ref{['boundradW']} isn't satisfied so our radially fuzzy D2 branes can't develop. $B_{r}$ is green where this bound is satisfied and the vacua admits non-abelian $\mathfrak{su}(2)$ radially fuzzy D2 branes, which are energetically favored over their abelian counterpart.