Sigma-model for Generalized Composite p-branes
Abstract
A multidimensional gravitational model containing several dilatonic scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 x M1 x ... x Mn, where Mi are Einstein spaces (i > 0). The block-diagonal metric is chosen and all fields and scale factors of the metric are functions on M0. For the forms composite (electro-magnetic) p-brane ansatz is adopted. The model is reduced to gravitating self-interacting sigma-model with certain constraints. In pure electric and magnetic cases the number of these constraints is m(m - 1)/2 where m is number of 1-dimensional manifolds among Mi. In the "electro-magnetic" case for dim M0 = 1, 3 additional m constraints appear. A family of "Majumdar-Papapetrou type" solutions governed by a set of harmonic functions is obtained, when all factor-spaces Mk are Ricci-flat. These solutions are generalized to the case of non-Ricci-flat M0 when also some additional "internal" Einstein spaces of non-zero curvature are added to M. As an example exact solutions for D = 11 supergravity and related 12-dimensional theory are presented.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.