Fluxbrane and S-brane solutions with polynomials related to rank-2 Lie algebras

摘要

Composite fluxbrane and S-brane solutions for a wide class of intersectionrules are considered. These solutions are defined on a product manifold R_{*} xM_1 x ... x M_n which contains n Ricci-flat spaces M_1, ..., M_n with1-dimensional factor spaces R_{*} and M_1. They are determined up to a set offunctions obeying non-linear differential equations equivalent to Toda-typeequations with certain boundary conditions imposed. Exact solutionscorresponding to configurations with two branes and intersections related tosimple Lie algebras C_2 and G_2 are obtained. In these cases, the functionsH_s(z), s =1,2, are polynomials of degrees (3, 4) and (6, 10), respectively, inagreement with a conjecture put forward previously in Ref., \cite{Iflux}. TheS-brane solutions under consideration, for special choices of the parameters,may describe an accelerating expansion of our 3-dimensional space and a smallenough variation of the effective gravitational constant.