SL(N+1,R) Toda Solitons in Supergravities

TL;DR

This paper constructs non-supersymmetric $(D-3)$-brane and instanton solutions in supergravity theories, demonstrating that their equations of motion can be expressed as $SL(N+1,R)$ Toda equations, and connects these to known supersymmetric solutions.

Contribution

It introduces a new class of solutions in supergravity theories by formulating their equations as $SL(N+1,R)$ Toda equations, extending the understanding of brane and instanton configurations.

Findings

Solutions are non-supersymmetric for generic charges.

Solutions reduce to known supersymmetric cases when charges vanish.

Equations of motion can be expressed as $SL(N+1,R)$ Toda equations.

Abstract

We construct $(D-3)$-brane and instanton solutions using $N \le 10-D$ one-form field strengths in $D$ dimensions, and show that the equations of motion can be cast into the form of the $SL(N+1,R)$ Toda equations. For generic values of the charges, the solutions are non-supersymmetric; however, they reduce to the previously-known multiply-charged supersymmetric solutions when appropriate charges vanish.