Multidimensional Classical and Quantum Cosmology with Intersecting p-branes

TL;DR

This paper develops a multidimensional cosmological model with intersecting p-branes, deriving classical and quantum solutions, and introduces generalized intersection rules linked to Toda lattices, with implications for higher-dimensional theories.

Contribution

It presents a new framework for analyzing multidimensional cosmology with intersecting p-branes, including solutions and generalized intersection rules related to Toda lattices.

Findings

Classical and quantum solutions for the model are obtained.

A non-orthogonal generalization of intersection rules is introduced.

Connections to higher-dimensional supergravity and F-theories are suggested.

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.