Classification of p-branes, NUTs, Waves and Intersections

TL;DR

This paper provides a comprehensive classification of supersymmetric p-brane solutions in supergravity theories across various dimensions, detailing their intersections, supersymmetry preservation, and U-duality structures.

Contribution

It introduces universal rules for supersymmetry fractions and classifies all p-brane intersections in D=10 and D=11 from lower-dimensional solutions.

Findings

Complete classification of multi-charge p-branes in supergravity

Universal rules for supersymmetry preservation

Mapping of U-duality multiplets to intersection structures

Abstract

We give a full classification of the multi-charge supersymmetric $p$-brane solutions in the massless and massive maximal supergravities in dimensions $D\ge2$ obtained from the toroidal reduction of eleven-dimensional supergravity. We derive simple universal rules for determining the fractions of supersymmetry that they preserve. By reversing the steps of dimensional reduction, the $p$-brane solutions become intersections of $p$-branes, NUTs and waves in D=10 or D=11. Having classified the lower-dimensional $p$-branes, this provides a classification of all the intersections in D=10 and D=11 where the harmonic functions depend on the space transverse to all the individual objects. We also discuss the structure of U-duality multiplets of $p$-brane solutions, and show how these translate into multiplets of harmonic and non-harmonic intersections.