HAL : hal-00138826, version 1

arXiv : hep-th/0503094

DOI : 10.1088/1126-6708/2005/06/025

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Journal of High Energy Physics 6, 025 (2005) 37 p

Special geometry of euclidean supersymmetry II. Hypermultiplets and the $c$-map

Christoph Mayer 1, Thomas Mohaupt 1, Frank Saueressig 2, Vicente Cortés 3

(2005)

We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in euclidean theories with rigid Script $N = 2$ supersymmetry. While the minkowskian para-$c$-map is obtained by dimensional reduction of the minkowskian vector multiplet lagrangian over time, the euclidean para-c-map corresponds to the dimensional reduction of the euclidean vector multiplet lagrangian. In both cases the resulting hypermultiplet target spaces are para-hyper-Kähler manifolds. We review and prove the relevant results of para-complex and para-hypercomplex geometry. In particular, we give a second, purely geometrical construction of both $c$-maps, by proving that the cotangent bundle $N = T*M$ of any affine special (para-)Kähler manifold $M$ is para-hyper-Kähler.

1 :	Theoretisch-Physikalisches Institut
	Universität Jena
2 :	Institute for Theoretical Physics and Spinoza Institute
	Spinoza Institute
3 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)

Domaine

:

Mathématiques/Géométrie différentielle Physique/Physique des Hautes Energies - Théorie

Mots Clés : Extended Supersymmetry – Differential and Algebraic Geometry

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Contributeur : Estelle Carciofi <>

Soumis le : Mardi 27 Mars 2007, 17:00:44

Dernière modification le : Mardi 15 Mai 2007, 11:42:38