The local supersymmetries of a stack of branes

TL;DR

This paper classifies BPS supergravity solutions with maximal local supersymmetry, highlighting the geometric nature of monopoles and polarised branes, while suggesting instantons involve non-abelian degrees of freedom beyond supergravity.

Contribution

It identifies the conditions under which brane solutions exhibit maximal local supersymmetry and distinguishes between geometric monopoles and non-geometric instantons.

Findings

Maximal supersymmetry solutions are geometric when the gauge group is maximally abelian.

Monopoles and polarised branes preserve local supercharges and are geometric.

Instantons involve non-abelian degrees of freedom not captured by supergravity.

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.