p-brane Solitons in Maximal Supergravities

TL;DR

The paper systematically classifies $p$-brane solitons in all maximal supergravities arising from $D=11$ supergravity, using KK dimensional reduction to derive complete bosonic Lagrangians and a brane-adapted framework. Supersymmetry properties are analyzed via Bogomol'nyi matrices derived from Nester forms, enabling an exhaustive catalog of supersymmetric solutions for 4-, 3-, and 2-form field strengths and a broad set of non-supersymmetric cases, including various dyonic configurations in $D=6$ and $D=4$. A central organizing principle is the dilaton scaling parameter $\Delta$, which, together with the participating field strengths, determines the metric, charges, and preserved supersymmetry. The results reveal a rich spectrum of solitons, including self-dual and massless limits, with detailed eigenvalue structures of the Bogomol'nyi matrices that encode the amount of unbroken supersymmetry. The work provides a comprehensive map of maximal supergravity p-branes across dimensions $4\le D\le 11$, clarifying how dualities, dualisations, and CS terms shape the solitonic landscape.

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.