Solutions with intersecting p-branes related to Toda chains

TL;DR

This paper derives solutions in multidimensional gravity involving intersecting p-branes, connecting them to Toda-like systems and exploring special cases related to A_m Toda chains, with solutions governed by harmonic functions and null-geodesics.

Contribution

It introduces a general class of solutions in multidimensional gravity with p-branes linked to Toda systems, including special cases related to A_m Toda chains.

Findings

Solutions are defined on product of Ricci-flat spaces and governed by harmonic functions.

Connections established between p-brane solutions and Toda-like equations.

Special solutions related to A_m Toda chains are analyzed.

Abstract

Solutions in multidimensional gravity with m p-branes related to Toda-like systems (of general type) are obtained. These solutions are defined on a product of n+1 Ricci-flat spaces M_0 x M_1 x...x M_n and are governed by one harmonic function on M_0. The solutions are defined up to the solutions of Laplace and Toda-type equations and correspond to null-geodesics of the (sigma-model) target-space metric. Special solutions relating to A_m Toda chains (e.g. with m =1,2) are considered.