Solitons on the Supermembrane

TL;DR

The paper analyzes solitons on the M2-brane in a hyper-Kähler background, deriving Bogomol'nyi-type energy bounds and showing lumps saturate $E=|T|$ while Q-kinks saturate $E=\sqrt{Q_0^2+Q^2}$, with both preserving half of the worldvolume supersymmetry. Lumps correspond to holomorphic maps with two active scalars, and Q-kinks arise from Scherk–Schwarz reduction along a holomorphic Killing vector, yielding a potential $V \sim |k|^2$. The authors provide a brane interpretation, linking lumps to finite-energy holomorphic intersections and Q-kinks to bound states, and give a dual IIB picture where Q-kinks are migrating (1,1) strings between D5-branes, with the charge structure encoded in a topological4-vector $Q=(\tilde{Q}_0,\mathbf{Q})$. These results connect worldvolume solitons to the central-charge structure of the membrane theory and illustrate how M-theory configurations map under dualities to IIB brane setups.

Abstract

Energy bounds are derived for planar and compactified M2-branes in a hyper-Kähler background. These bounds are saturated, respectively, by lump and Q-kink solitons, which are shown to preserve a half of the worldvolume supersymmetry. The Q-kinks have a dual IIB interpretation as strings that migrate between fivebranes.