Composite p-branes in various dimensions

TL;DR

This paper reviews an algebraic method for constructing composite p-brane solutions across various dimensions, simplifying the equations to algebraic forms and demonstrating the superposition of harmonic functions for multiple branes.

Contribution

It introduces a unified algebraic approach to find composite p-brane solutions in arbitrary dimensions, extending known solutions and clarifying the superposition rule.

Findings

Solutions involve n independent harmonic functions

Equations reduce to Laplace and algebraic forms

Demonstrates superposition rule in diverse dimensions

Abstract

We review an algebraic method of finding the composite p-brane solutions for a generic Lagrangian, in arbitrary spacetime dimension, describing an interaction of a graviton, a dilaton and one or two antisymmetric tensors. We set the Fock--De Donder harmonic gauge for the metric and the "no-force" condition for the matter fields. Then equations for the antisymmetric field are reduced to the Laplace equation and the equation of motion for the dilaton and the Einstein equations for the metric are reduced to an algebraic equation. Solutions composed of n constituent p-branes with n independent harmonic functions are given. The form of the solutions demonstrates the harmonic functions superposition rule in diverse dimensions. Relations with known solutions in D=10 and D=11 dimensions are discussed.