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arXiv · hep-th/0312189

Exact solutions for Bianchi type cosmological metrics, Weyl orbits of E_{8(8)} subalgebras and p--branes

P. Fré·K. Rulik·M. Trigiante
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Abstract

In this paper we pursue further a programme initiated in a previous work and aimed at the construction, classification and property investigation of time dependent solutions of supergravity (superstring backgrounds) through a systematic exploitation of U-duality hidden symmetries. This is done by first reducing to D=3 where the bosonic part of the theory becomes a sigma model on E_{8(8)}/SO(16), solving the equations through an algorithm that produces general integrals for any chosen regular subalgebra G_r of E_{8(8)} and then oxiding back to D=10. Different oxidations and hence different physical interpretations of the same solutions are associated with different embeddings of G_r. We show how such embeddings constitute orbits under the Weyl group and we study the orbit space. This is relevant to associate candidate superstring cosmological backgrounds to space Dp-brane configurations that admit microscopic descriptions. In particular in this paper we show that there is just one Weyl orbit of A_r subalgebras for r < 6$. The orbit of the previously found A_2 solutions, together with space--brane representatives contains a pure metric representative that corresponds to homogeneous Bianchi type 2A cosmologies in D=4 based on the Heisenberg algebra. As a byproduct of our methods we obtain new exact solutions for such cosmologies with and without matter. We present a thorough investigation of their properties.

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P. Fré, K. Rulik, M. Trigiante. 2003-12-16. Exact solutions for Bianchi type cosmological metrics, Weyl orbits of E_{8(8)} subalgebras and p--branes. https://doi.org/10.1016/j.nuclphysb.2004.06.011

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