Toroidal AdS Charged Branes and Toda Equations

TL;DR

This paper derives static charged AdS brane solutions with toroidal symmetry by transforming their equations of motion into Toda type equations, revealing their dependence on mass, charges, and dilaton coupling.

Contribution

It introduces a method to reduce charged brane equations in AdS space to Toda equations and constructs explicit static solutions with toroidal symmetry.

Findings

Solutions characterized by mass, charges, and dilaton coupling

Equations of motion reduced to Toda type equations

Static solutions with toroidal symmetry constructed

Abstract

In this note, we consider the equations of motion for charged branes in AdS space and show that they can be cast into one-dimensional coupled Toda type. Then we solve the equations of motion to construct static charged AdS brane solutions which are invariant under translation along $p$ directions and have toroidal symmetry. The solutions are described by mass, charges and a dilaton coupling constant.