Fluxbrane and S-brane Solutions with Polynomials Related to Rank-2 Lie Algebras

Composite fluxbrane and S -brane solutions for a wide class of intersection rules are considered. These solutions are defined on a product manifold R∗×M1×. . .×Mn which contains n Ricci-flat spaces M1, . . . , Mn with 1-dimensional factor spaces R∗ and M1 . They are determined up to a set of functions obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. Exact solutions corresponding to configurations with two branes and intersections related to simple Lie algebras C2 and G2 are obtained. In these cases, the functions Hs(z) , s = 1, 2, are polynomials of degrees (3, 4) and (6, 10), respectively, in agreement with a conjecture put forward previously in Ref. [1]. The S -brane solutions under consideration, for special choices of the parameters, may describe an accelerating expansion of our 3-dimensional space and a small enough variation of the effective gravitational constant.