Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-08-26
Nucl.Phys. B660 (2003) 169-193
Physics
High Energy Physics
High Energy Physics - Theory
Version with 23 pages, no figures, the one form corresponding to the 3 pole solution are expressed in another way
Scientific paper
10.1016/S0550-3213(03)00235-9
In the present work the Calderbank-Pedersen description of four dimensional manifolds with self-dual Weyl tensor is used to obtain examples of quaternionic-kahler metrics with two commuting isometries. The eigenfunctions of the hyperbolic laplacian are found by use of Backglund transformations acting over solutions of the Ward monopole equation. The Bryant-Salamon construction of $G_2$ holonomy metrics arising as $R^3$ bundles over quaternionic-kahler base spaces is applied to this examples to find internal spaces of the M-theory that leads to an N=1 supersymmetry in four dimensions. Type IIA solutions will be obtained too by reduction along one of the isometries. The torus symmetry of the base spaces is extended to the total ones.
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