Intersecting Branes

TL;DR

Gauntlett surveys BPS intersecting brane configurations in M-theory and Type II string theory, focusing on orthogonal intersections and the harmonic function rule to construct multi-brane solutions while preserving supersymmetry. It develops the connection between M-brane intersections and their IIA/IIB descendants via dimensional reduction and dualities, and extends to non-orthogonal intersections using Taub-NUT and toric hyper-Kähler geometries, yielding branes intersecting at angles with $3/16$ SUSY. The work also discusses dynamic aspects such as branes ending on branes and branes within branes, and shows how intersecting configurations lead to black hole solutions with non-zero horizon area in $D=4,5$, linking microscopic states to macroscopic entropy. Altogether, it clarifies how dualities, holonomy, and hyper-Kähler geometry underpin the structure and supersymmetry of complex brane intersections, while pointing to open problems in achieving fully localised solutions and deeper field theory applications.

Abstract

BPS configurations of intersecting branes have many applications in string theory. We attempt to provide an introductory and pedagogical review of supergravity solutions corresponding to orthogonal BPS intersections of branes with an emphasis on eleven and ten space-time dimensions. Recent work on BPS solutions corresponding to non-orthogonally intersecting branes is also discussed. These notes are based on lectures given at the APCTP Winter School "Dualities of Gauge and String Theories", Korea, February 1997.