Sigma-model for the 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 = M 0 × M 1 × . . . × M n , where M i are Einstein spaces (i ≥ 1). The block-diagonal metric is chosen and all fields and scale factors of the metric are functions on M 0 . 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 n 1 (n 1 − 1)/2 where n 1 is number of 1-dimensional manifolds among M i . In the "electro-magnetic" case for dimM 0 = 1, 3 additional n 1 constraints appear. A family of "MajumdarPapapetrou type" solutions governed by a set of harmonic functions is obtained, when all factor-spaces M ν are Ricci-flat. These solutions are generalized to the case of non-Ricci-flat M 0 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.

Composite S-Brane Solutions on the Product of Ricci-Flat Spaces

“…Here we consider the minisuperspace covariant relations from [5,22] for the sake of completeness. Let…”

“…The scalar product from [22] reads (U s , U s ′ ) = 0, (2.37) for s = s ′ . The linear and quadratic constraints from (2.26) and (2.28), respectively, read in minisuperspace covariant form as follows: …”

“…The solutions presented above are valid if two restrictions on the sets of composite p -branes are satisfied [7]. These restrictions guarantee the block-diagonal form of the energy-momentum tensor and the existence of the sigma-model representation (without additional constraints) [22].…”

Composite fluxbranes with general intersections

“…These restrictions guarantee the block-diagonal form of the energy-momentum tensor and the existence of the sigma-model representation (without additional constraints) [35,34]. Let us denote w 1 ≡ {i|i ∈ {1, .…”

“…Here we remind a minisuperspace covariant form of constraints using so called U s -vectors [35]. The constraints (2.30) may be written in the following form…”