A World-Volume Perspective on the Recombination of Intersecting Branes

TL;DR

This work presents a world-volume field-theory description of brane recombination for supersymmetric intersections, showing that $F$- and $D$-flatness in a reduced superspace naturally yield calibration conditions for the resulting geometry. Eight-supercharge cases yield holomorphic curves on the Higgs branch (e.g. $wy=c$), while four-supercharge triple intersections produce special Lagrangian three-folds, with certain configurations reducing to holomorphic curves times a line. Impurity fields localized at intersections drive recombination, and explicit analyses of D3/D3' and D6-brane intersections clarify the Coulomb versus Higgs branches and their geometric realizations. A scattering analysis of massless modes on the recombined brane demonstrates how deformation controls transmission between asymptotic regions, reinforcing the physical picture of brane merging into a single calibrated object. Overall, the paper connects defect field theory to calibrated geometry, offering a concrete field-theoretic account of brane recombination with potential links to M-theory and G2 holonomy constructions.

Abstract

We study brane recombination for supersymmetric configurations of intersecting branes in terms of the world-volume field theory. This field theory contains an impurity, corresponding to the degrees of freedom localized at the intersection. The Higgs branch, on which the impurity fields condense, consists of vacua for which the intersection is deformed into a smooth calibrated manifold. We show this explicitly using a superspace formalism for which the calibration equations arise naturally from F- and D-flatness.