Intersecting brane solutions in string and M-theory

TL;DR

The paper surveys supersymmetric intersecting brane configurations in string and M-theory, detailing how Killing spinor projections and calibrations constrain allowed intersections and guide solution-building. It introduces the harmonic-function rules for constructing smeared backgrounds, then extends to partially localised and near-horizon solutions, illustrating the approach with black hole entropy counts and brane-probe checks. A central theme is the interplay between worldvolume descriptions and supergravity, including the AdS/CFT framework and Hanany–Witten constructions that relate brane setups to four-dimensional N=2 gauge theories, their moduli spaces, and gravity duals. The review also discusses fully localised solutions, special holonomy backgrounds, and the ongoing challenges in obtaining general localised intersecting-brane metrics, highlighting the deep connections between geometry, holography, and gauge dynamics. Overall, intersecting branes provide a versatile toolkit for understanding nonperturbative aspects of gauge theories and quantum gravity.

Abstract

We review various aspects of configurations of intersecting branes, including the conditions for preservation of supersymmetry. In particular, we discuss the projection conditions on the Killing spinors for given brane configurations and the relation to calibrations. This highlights the close connection between intersecting branes and branes wrapping supersymmetric cycles as well as special holonomy manifolds. We also explain how these conditions can be used to find supergravity solutions without directly solving the Einstein equations. The description of intersecting branes is considered both in terms of the brane worldvolume theories and as supergravity solutions. There are well-known simple procedures (harmonic function rules) for writing down the supergravity solutions for supersymmetric configurations of orthogonally intersecting branes. However, such solutions involve smeared or delocalised branes. We describe several methods of constructing solutions with less smearing, including some fully localised solutions. Some applications of these supergravity solutions are also considered - in particular the study of black holes and gauge theories.