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Toric hyperkahler manifolds with quaternionic Kahler bases and supergravity solutions | | O.P. Santillan
; A.G. Zorin
; | | Date: |
14 Dec 2003 | | Journal: | Commun.Math.Phys. 255 (2005) 33-59 | | Subject: | High Energy Physics - Theory; Mathematical Physics | hep-th math-ph math.MP | | Abstract: | In the present work some examples of toric hyperkahler metrics in eight dimensions are constructed. First it is described how the Calderbank-Pedersen metrics arise as a consequence of the Joyce description of selfdual structures in four dimensions, the Jones-Tod correspondence and a result due to Tod and Przanowski. It is also shown that any quaternionic Kahler metric with $T^2$ isometry is locally isometric to a Calderbank-Pedersen one. The Swann construction of hyperkahler metrics in eight dimensions is applied to them to find hyperkahler examples with $U(1) imes U(1)$ isometry. The connection with the Pedersen-Poon toric hyperkahler metrics is explained and it is shown that there is a class of solutions of the generalized monopole equation in $mathbb{R}^2 otimes Immathbb{H}$ related to eigenfunctions of certain linear equation. This hyperkahler examples are lifted to solutions of the D=11 supergravity and type IIA and IIB backgrounds are found by use of dualities. As before, all the description is achieved in terms of a single eigenfunction F. Some explicit F are found, together with the Toda structure corresponding to the trajectories of the Killing vectors of the Calderbank-Pedersen bases. | | Source: | arXiv, hep-th/0401098 | | Services: | Forum | Review | PDF | Favorites | |
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