Multidimensional classical and quantum cosmology with intersecting p-branes

Abstract

Multidimensional cosmological model describing the evolution of (n + 1) Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane Ansatz is adopted the field equations are reduced to the equations for Toda-like system. The Wheeler-De Witt equation is obtained. In the case when n "internal" spaces are Ricci-flat, one space M 0 has a non-zero curvature, and all p-branes do not "live" in M 0 , the classical and quantum solutions are obtained if certain orthogonality relations on parameters are imposed. Spherically-symmetric solutions with intersecting non-extremal p-branes are singled out. A non-orthogonal generalization of intersection rules corresponding to (open, closed) Toda lattices is obtained. A chain of bosonic D ≥ 11 models (that may be related to hypothetical higher dimensional supergravities and F -theories) is suggested.

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…”

“…those of superstring or supergravity origin (see, for example [4] and references therein). These solutions deal with time-dependent scale factors of internal spaces (for reviews see [5,6,8,9]) and contain as a special case the so-called S-brane solutions [10], i.e. space like analogues of D -branes [18], see for example [11,12,13,14,15,16,17] and references therein.…”

On Brane Solutions with Intersection Rules Related to Lie Algebras

“…From a pure mathematical point of view, these solutions may be obtained from sigma-models or Toda chains corresponding to certain non-singular KM algebras. The information about the (hidden) KM algebra is encoded in intersection rules, which relate the dimensions of brane intersections with non-diagonal components of the generalized Cartan matrix A [55]. We deal here with generalized Cartan matrices of the form:…”

“…Some examples of this are given below (see Section 5). For D = 11 supergravity and ten-dimensional I I A , I IB supergravities, all (U s , U s ) = 2 [44,55] and corresponding KM algebras are simply laced. It was shown in our papers [29][30][31] that the inequality (U s , U s ) > 0 is a necessary condition for the formation of the billiard wall (ifone approaches the singularity) by the s-th matter source (e.g., a fluid component or a brane).…”

Black-brane solution for A3 algebra

“…More general spherically symmetric solutions were obtained in [14] using the sigma-model approach from [7,13,4]. For another (algebraic) approach see also [5,6,9] and references therein.…”