BPS Bounds for Worldvolume Branes

TL;DR

Gauntlett, Gomis, and Townsend develop BPS-type bounds for worldvolume branes, showing that central charges in the worldvolume SUSY algebra (Y and Z) bound p-volume tensions via density integrals such as $Y=\int dX\wedge H$ and $Z=\frac{i}{2}\int dU\wedge dŪ$. They derive explicit bounds and first-order BPS equations for a spectrum of solitons, including abelian vortices, BIons, BI instantons, BI dyons, non-abelian vortices, and Nahm data, covering both Abelian and non-Abelian cases and their D- and M-brane realizations. The results unify spacetime-intersection interpretations with worldvolume dynamics by linking charges to holomorphic or harmonic field configurations and Nahm data, and they extend to string boundaries on M-5-branes. The paper also discusses unresolved intersections, duality-related cases, and suggests the possible role of higher-order BI terms in certain backgrounds, underscoring the continued richness of brane solitons in string/M-theory.

Abstract

The worldvolume field equations of M-branes and D-branes are known to admit p-brane soliton solutions. These solitons are shown to saturate a BPS-type bound on their p-volume tensions, which are expressed in terms of central charges that are expected to appear in the worldvolume supertranslation algebra. The cases we consider include vortices, `BIons', instantons and dyons (both abelian and non-abelian), and the string boundaries of M-2-branes in the M-5-brane.