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

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.

40 pages,0 figure Minor corrected typos

References in corpus (4)

• Hypermultiplets, domain walls and supersymmetric attractors
• Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry
• Gaugings and other supergravity tools of p-brane physics
• Quaternionic Extension of the Double Taub-NUT Metric

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