p-brane Solitons in Maximal Supergravities

TL;DR

This paper constructs and classifies p-brane soliton solutions in all maximal supergravity theories from 4 to 11 dimensions, analyzing their supersymmetry properties and providing a comprehensive list of solutions with various field strengths.

Contribution

It provides a unified construction of p-brane solutions across all maximal supergravities derived from D=11 supergravity, including their supersymmetry analysis and explicit solution classification.

Findings

Complete bosonic Lagrangians for all theories in the specified dimensions.

Exhaustive list of supersymmetric p-brane solutions with various field strengths.

Identification of indefinite signature in Bogomol'nyi matrices for dyonic solutions.

Abstract

In this paper, we give a construction of $p$-brane solitons in all maximal supergravity theories in $4\le D \le 11$ dimensions that are obtainable from $D=11$ supergravity by dimensional reduction. We first obtain the full bosonic Lagrangians for all these theories in a formalism adapted to the $p$-brane soliton construction. The solutions that we consider involve one dilaton field and one antisymmetric tensor field strength, which are in general linear combinations of the basic fields of the supergravity theories. We also study the supersymmetry properties of the solutions by calculating the eigenvalues of the Bogomol'nyi matrices, which are derived from the commutators of the supercharges. We give an exhaustive list of the supersymmetric $p$-brane solutions using field strengths of all degrees $n=4,3,2,1$, and the non-supersymmetric solutions for $n=4,3,2$. As well as studying elementary and solitonic solutions, we also discuss dyonic solutions in $D=6$ and $D=4$. In particular, we find that the Bogomol'nyi matrices for the supersymmetric massless dyonic solutions have indefinite signature.