Supersymmetric Fivebrane Solitons

TL;DR

This work analyzes how the D=11 M5-brane worldvolume can support supersymmetric solitons with a nonzero self-dual 3-form $H$, building solitons from calibrated M5 embeddings, self-dual strings, and instanton (neutral) strings. Using both Hamiltonian and covariant formalisms, the authors derive BPS bounds and projection conditions, and construct explicit configurations such as traveling waves on calibrated surfaces, instanton strings on calibrated submanifolds, and systems with two intersecting self-dual strings. They show how these solitons can be superposed on calibrated geometries and how their energies are governed by harmonic functions and instanton moduli, with dimensional reduction to D4-brane DBI theory and potential non-Abelian extensions. The results illuminate the rich non-linear dynamics of the fivebrane worldvolume and its spacetime intersections, offering a laboratory for brane interactions and calibrations in M-theory.

Abstract

We study the conditions for the fivebrane worldvolume theory in D=11 to admit supersymmetric solitons with non-vanishing self-dual three-form. We construct some new soliton solutions consisting of ``superpositions'' of calibrated surfaces, self-dual strings and instantons.