BPS Branes in Supergravity

TL;DR

The paper classifies and analyzes BPS p-brane solutions in maximal supergravity, deriving their charges, masses, and supersymmetry properties from a unified p-brane ansatz. By reducing to single-charge truncations and exploiting diagonal and vertical Kaluza–Klein reductions, it shows how D=11 origins generate a web of lower-dimensional branes, including domain walls and black branes, while preserving a portion of supersymmetry. It reveals how p-form charges saturate Bogomol’nyi bounds, how duality groups organize charge lattices, and how sigma-model dynamics encode multi-brane bound states and instanton-like reductions. The work connects classical supergravity solutions to quantum dualities, charge quantisation, and the broader M-theory framework, highlighting the geometric and algebraic structure underlying brane dynamics and their role as stable, BPS states in string theory.

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 Poincaré-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 $σ$-models; and the target-space geometry of BPS instanton solutions obtained by the dimensional reduction of static $p$-branes.

Figures (7)

• Figure 1: Carter-Penrose diagram for the $D=11$ elementary/electric 2-brane solution.
• Figure 2: The $D=11$ elementary/electric 2-brane solution interpolates between flat space at ${\cal J}^\pm$ and $(\hbox{AdS})_4\times{\cal S}^7$ at the horizon.
• Figure 3: Carter-Penrose diagram for the solitonic/magnetic 5-brane solution.
• Figure 4: Different choices of charge integration volume "capturing" the current $J_{[3]}$.
• Figure 5: Finite $p$-brane not captured by $\partial{\cal M}$, giving zero charge.