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U(1) x U(1) Quaternionic Metrics from Harmonic Superspace

Pierre-Yves Casteill·Evgeny Ivanov·Galliano Valent
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Abstract

We construct, using harmonic superspace and the quaternionic quotient approach, a quaternionic-Kähler extension of the most general two centres hyper-Kähler metric. It possesses $U(1)\times U(1)$ isometry, contains as special cases the quaternionic-Kähler extensions of the Taub-NUT and Eguchi-Hanson metrics and exhibits an extra one-parameter freedom which disappears in the hyper-Kähler limit. Some emphasis is put on the relation between this class of quaternionic-Kähler metrics and self-dual Weyl solutions of the coupled Einstein-Maxwell equations. The relation between our explicit results and the recent general ansatz of Calderbank and Pedersen for quaternionic-Kähler metrics with $U(1)\times U(1)$ isometries is traced in detail.

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Pierre-Yves Casteill, Evgeny Ivanov, Galliano Valent. 2002-03-25. U(1) x U(1) Quaternionic Metrics from Harmonic Superspace. https://doi.org/10.1016/s0550-3213(02)00013-5

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