The local supersymmetries of a stack of branes

TL;DR

The paper analyzes local supersymmetry enhancement in stacks of branes through the non-abelian Born-Infeld/Wess-Zumino framework, identifying sixteen local supersymmetries in monopole and brane-polarization setups while finding instantons lack this property. It employs Taylor–Van Raamsdonk currents and κ-symmetry to extract brane densities and projec tors, revealing a rich, dipole-dominated structure that splits into regions on and between branes. A key result is that three-charge monopoles (D2–D4–P) preserve the sixteen local supersymmetries, suggesting their backreaction could admit horizonless microstate geometries in supergravity, unlike D1–D5–P instanton frames. The work emphasizes duality-frame dependence of geometric realization of internal brane excitations and provides concrete density patterns to guide future supergravity constructions of microstates. Overall, it strengthens the view that monopole-like bound states furnish geometric microstate building blocks, while pure non-abelian instantons remain non-geometric from a supergravity perspective.

Abstract

Local supersymmetries have been a guiding principle to construct smooth horizonless supergravity solutions. By computing brane densities from the brane low-energy effective action, we classify the BPS solutions that have the maximal local supersymmetry structure, with sixteen supersymmetries. We find that whenever the gauge group is broken to its maximal abelian subgroup, the brane construction becomes purely geometric and one can identify the preserved local supercharges. This class of solution includes two- and three-charge monopoles, and polarised branes. On the contrary, we show that instantons involve pure non-abelian degrees of freedom that cannot have a geometric interpretation. Hence, we conjecture that such instantons cannot be fully captured by supergravity.

Figures (4)

• Figure 1: In blue, the shape taken by the D3-brane configuration induced by the scalar field $\Phi$ of a 't Hooft-Polyakov monopole. There is a spherical symmetry in the directions $(x^1,x^2,x^3)$, and only the radius $r$ is represented here. The two D3-branes meet at $r=0$ and $z=0$. We represent in red the asymptotic separation of the two D3 branes. As we will show later, there exists a D1-brane current along the $z$ direction (represented by the black arrow), at all points in the region in between the two D3 branes. On the blue line there are densities of D1 and D3 branes.
• Figure 2: Diagram of the brane densities on top of the branes. The global charges, whose charges do not vanish when summed over both branches of the D3 locus, are encircled. The 'glues', whose charges are opposite on either branch, are represented below the line linking the 'main branes'.
• Figure 3: Triality of the brane densities. The global brane charges are at the corners of the triangle. Each pair of global brane charges is linked by a pair of glues.
• Figure 4: Brane densities in between the D4 branes.