Intersecting brane solutions in string and M-theory

TL;DR

This paper reviews intersecting brane configurations in string and M-theory, focusing on supersymmetry conditions, solution construction methods, and applications to black holes and gauge theories.

Contribution

It provides a comprehensive overview of methods for constructing both smeared and localized intersecting brane solutions and explores their applications in theoretical physics.

Findings

Established projection conditions for supersymmetry preservation.

Described methods for constructing localized supergravity solutions.

Discussed applications to black hole physics and gauge theories.

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.