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

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

2001-10-30

arxiv.org/abs/hep-th/0110280v2

Nucl.Phys. B627 (2002) 403-444

Physics

High Energy Physics

High Energy Physics - Theory

40 pages,0 figure Minor corrected typos

Scientific paper

10.1016/S0550-3213(02)00013-5

We construct, using harmonic superspace and the quaternionic quotient approach, a quaternionic-K\"ahler extension of the most general two centres hyper-K\"ahler metric. It possesses $U(1)\times U(1)$ isometry, contains as special cases the quaternionic-K\"ahler extensions of the Taub-NUT and Eguchi-Hanson metrics and exhibits an extra one-parameter freedom which disappears in the hyper-K\"ahler limit. Some emphasis is put on the relation between this class of quaternionic-K\"ahler 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-K\"ahler metrics with $U(1)\times U(1)$ isometries is traced in detail.

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