Jan Rosseel and Antoine Van Proeyen 2004 Class. Quantum Grav. 21 5503 doi:10.1088/0264-9381/21/23/013
Hypermultiplets and hypercomplex geometry from six to three dimensions
Jan Rosseel and Antoine Van Proeyen
Show affiliationsThe formulation of hypermultiplets that has been developed for five-dimensional matter multiplets is by dimensional reductions translated into the appropriate spinor language for six and four dimensions. We also treat the theories without actions that have the geometrical structure of hypercomplex geometry. The latter is the generalization of hyper-Kähler geometry that does not require a Hermitian metric and hence corresponds to field equations without action. The translation tables of this paper allow the direct application of superconformal tensor calculus for the hypermultiplets using the available Weyl multiplets in six and four dimensions. Furthermore, the hypermultiplets in three dimensions that result from reduction of vector multiplets in four dimensions are considered, leading to a superconformal formulation of the c-map and an expression for the main geometric quantities of the hyper-Kähler manifolds in the image of this map.
- PACS
- MSC
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53C26 Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry
- Subjects
- Dates
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Issue 23 (7 December 2004)
Received 11 June 2004, in final form 6 October 2004
Published 16 November 2004
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Hypermultiplets and hypercomplex geometry from six to three dimensions
Jan Rosseel and Antoine Van Proeyen 2004 Class. Quantum Grav. 21 5503
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