Intersecting p-brane Solutions in Multidimensional Gravity and M-theory

TL;DR

This paper develops a multidimensional gravity model with intersecting p-brane solutions, providing new explicit solutions and exploring their properties within M-theory and supergravity frameworks.

Contribution

It introduces a sigma-model representation for intersecting p-branes in a multidimensional setting and constructs a family of solutions, including special cases related to Diophantus equations.

Findings

Derived a sigma-model for the multidimensional gravity with scalar fields and forms.

Constructed a family of Majumdar-Papapetrou type solutions with Ricci-flat manifolds.

Presented explicit intersecting p-brane solutions, including a D=11 supergravity example.

Abstract

Multidimensional gravitational model on the manifold $M = M_0 \times \prod_{i=1}^{n} M_i$, where $M_i$ are Einstein spaces ($i \geq 1$), is considered. The action contains $m = 2^n -1$ dilatonic scalar fields $\phi^I$ and $m$ (antisymmetric) forms $A^I$. When all fields and scale factors of the metric depend (essentially) on the point of $M_0$ and any $A^I$ is "proportional" to the volume form of submanifold $M_{i_1} \times ... \times M_{i_k}$, $1 \leq i_1 < ... < i_k \leq n$, the sigma-model representation is obtained. A family of "Majumdar-Papapetrou type" solutions are obtained, when all $M_{\nu}$ are Ricci-flat. A special class of solutions (related to the solution of some Diophantus equation on dimensions of $M_{\nu}$) is singled out. Some examples of intersecting p-branes (e.g. solution with seven Euclidean 2-branes for D = 11 supergravity) are considered.}