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arXiv · hep-th/0401098

Toric hyperkahler manifolds with quaternionic Kahler bases and supergravity solutions

O. P. Santillan·A. G. Zorin
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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 $U(1)\times U(1)$ 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 $\mathbb{R}^2 \otimes Im\mathbb{H}$ 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.

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BibTeXRIS

O. P. Santillan, A. G. Zorin. 2004-07-19. Toric hyperkahler manifolds with quaternionic Kahler bases and supergravity solutions. https://doi.org/10.1007/s00220-004-1250-0

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