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

TL;DR

This paper constructs exact fluxbrane and S-brane solutions on product manifolds, linking polynomial functions to rank-2 Lie algebras, and explores their implications for cosmology and gravitational constant variation.

Contribution

It provides explicit solutions related to simple Lie algebras C_2 and G_2, confirming a conjecture about polynomial functions in fluxbrane and S-brane configurations.

Findings

Exact solutions with polynomial functions of degrees 3, 4, 6, and 10 are obtained.

Solutions can describe accelerating expansion of the universe.

The models imply small variations in the effective gravitational constant.

Abstract

Composite fluxbrane and S-brane solutions for a wide class of intersection rules are considered. These solutions are defined on a product manifold R_{*} x M_1 x ... x M_n which contains n Ricci-flat spaces M_1, ..., M_n with 1-dimensional factor spaces R_{*} and M_1. 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 C_2 and G_2 are obtained. In these cases, the functions H_s(z), s =1,2, are polynomials of degrees (3, 4) and (6, 10), respectively, in agreement with a conjecture put forward previously in Ref., \cite{Iflux}. 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.