HAL : hal-00473312, version 1
 arXiv : hep-th/9212155
 Harmonic space and quaternionic manifolds
 (29/12/1992)
 We find a principle of harmonic analyticity underlying the quaternionic (quaternion-Kähler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local $Sp(1)$ group and an extra rigid $SU(2)$ group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to $N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic potentials. Coordinates of the analytic subspace are identified with superfields describing $N=2$ matter hypermultiplets and a compensating hypermultiplet of $N=2$ supergravity. As an illustration we present the potentials for the symmetric quaternionic spaces.
 1 : Institut de Physique Nucléaire d'Orsay (IPNO) CNRS : UMR8608 – IN2P3 – Université Paris XI - Paris Sud 2 : Fédération de Recherche des Unités de MAthématiques de Marseille (FRUMAM) CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Paul Cézanne - Aix-Marseille III – Université de Toulon : EA2134
 Domaine : Physique/Physique des Hautes Energies - Théorie
 Lien vers le texte intégral : http://fr.arXiv.org/abs/hep-th/9212155
 hal-00473312, version 1 http://hal.archives-ouvertes.fr/hal-00473312 oai:hal.archives-ouvertes.fr:hal-00473312 Contributeur : Oleg Ogievetsky <> Soumis le : Jeudi 15 Avril 2010, 10:22:57 Dernière modification le : Jeudi 15 Avril 2010, 10:22:57