Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 070, 34 pages      arXiv:0810.0196      http://dx.doi.org/10.3842/SIGMA.2009.070

On Brane Solutions Related to Non-Singular Kac-Moody Algebras

Vladimir D. Ivashchuk and Vitaly N. Melnikov
Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Str., Moscow 119361, Russia
Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russia

Received October 01, 2008, in final form June 15, 2009; Published online July 07, 2009

Abstract
A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 × M1 × ... × Mn, where Mi are Einstein spaces (i ≥ 1). The sigma-model approach and exact solutions with intersecting composite branes (e.g. solutions with harmonic functions, S-brane and black brane ones) with intersection rules related to non-singular Kac-Moody (KM) algebras (e.g. hyperbolic ones) are reviewed. Some examples of solutions, e.g. corresponding to hyperbolic KM algebras: H2(q,q), AE3, HA2(1), E10 and Lorentzian KM algebra P10 are presented.

Key words: Kac-Moody algebras; S-branes; black branes; sigma-model; Toda chains.

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