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

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 $ϕ^I$ 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 &#34;proportional&#34; 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 &#34;Majumdar-Papapetrou type&#34; solutions are obtained, when all $M_ν$ are Ricci-flat. A special class of solutions (related to the solution of some Diophantus equation on dimensions of $M_ν$) is singled out. Some examples of intersecting p-branes (e.g. solution with seven Euclidean 2-branes for D = 11 supergravity) are considered.}