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On Symmetries of Target Space for Sigma-model of p-brane Origin

V. D. Ivashchuk
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Abstract

The target space M for the sigma-model appearing in theories with p-branes is considered. It is proved that M is a homogeneous space G/H. It is symmetric if and only if the U-vectors governing the sigma-model metric are either coinciding or mutually orthogonal. For nonzero noncoinciding U-vectors the Killing equations are solved. Using a block-orthogonal decomposition of the set of the U-vectors it is shown that under rather general assumptions the algebra of Killing vectors is a direct sum of several copies of sl(2,R) algebras (corresponding to 1-vector blocks), several solvable Lie algebras (corresponding to multivector blocks) and the Killing algebra of a flat space. The target space manifold is decomposed in a product of a flat space, several 2-dimensional spaces of constant curvature (e.g. Lobachevsky space, part of anti-de Sitter space) and several solvable Lie group manifolds.

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V. D. Ivashchuk. 1998-08-08. On Symmetries of Target Space for Sigma-model of p-brane Origin. https://arxiv.org/abs/hep-th/9804102

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