BPS Branes in Supergravity

TL;DR

This review discusses classical supergravity solutions known as BPS branes, highlighting their properties, charge relations, supersymmetry preservation, and their roles in dualities and compactifications within string theory.

Contribution

It provides a comprehensive overview of BPS p-brane solutions in supergravity, including their structure, dualities, and geometric aspects, advancing understanding of their role in string theory.

Findings

BPS solutions saturate energy bounds and carry p-form charges.

Relations between mass, charge, and supersymmetry preservation are detailed.

Duality symmetries and compactification effects on p-branes are analyzed.

Abstract

This review considers the properties of classical solutions to supergravity theories with partially unbroken supersymmetry. These solutions saturate Bogomol'ny-Prasad-Sommerfield bounds on their energy densities and are the carriers of the $p$-form charges that appear in the supersymmetry algebra. The simplest such solutions have the character of $(p+1)$-dimensional Poincar\'e-invariant hyperplanes in spacetime, i.e. $p$-branes. Topics covered include the relations between mass densities, charge densities and the preservation of unbroken supersymmetry; interpolating-soliton structure; diagonal and vertical Kaluza-Klein reduction families; multiple-charge solutions and the four D=11 elements; duality-symmetry multiplets; charge quantisation; low-velocity scattering and the geometry of worldvolume supersymmetric $\sigma$-models; and the target-space geometry of BPS instanton solutions obtained by the dimensional reduction of static $p$-branes.