Special geometry in hypermultiplets

Abstract

We give a detailed analysis of pairs of vector and hypermultiplet theories with N=2 supersymmetry in four spacetime dimensions that are related by the (classical) mirror map. The symplectic reparametrizations of the special Kähler space associated with the vector multiplets induce corresponding transformations on the hypermultiplets. We construct the Sp(1)$\times$Sp($n$) one-forms in terms of which the hypermultiplet couplings are encoded and exhibit their behaviour under symplectic reparametrizations. Both vector and hypermultiplet theories allow vectorial central charges in the supersymmetry algebra associated with integrals over the Kähler and hyper-Kähler forms, respectively. We show how these charges and the holomorphic BPS mass are related by the mirror map.

Latex 36 pp. A few minor corrections

References in corpus (5)

• Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces
• Hyper-Kahler manifolds and multiply-intersecting branes
• Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold

Cited by in corpus (37)

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• Special Geometry of Euclidean Supersymmetry I: Vector Multiplets
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• Special Geometry of Euclidean Supersymmetry IV: the local c-map