Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-11-23
Commun.Math.Phys. 262 (2006) 411-457
Physics
High Energy Physics
High Energy Physics - Theory
54 pages, 2 figures; v2: small corrections, version to be published in CMP; v3: changes of statement on (3.5)
Scientific paper
10.1007/s00220-005-1475-6
We review the general properties of target spaces of hypermultiplets, which are quaternionic-like manifolds, and discuss the relations between these manifolds and their symmetry generators. We explicitly construct a one-to-one map between conformal hypercomplex manifolds (i.e. those that have a closed homothetic Killing vector) and quaternionic manifolds of one quaternionic dimension less. An important role is played by '\xi-transformations', relating complex structures on conformal hypercomplex manifolds and connections on quaternionic manifolds. In this map, the subclass of conformal hyper-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds. We relate the curvatures of the corresponding manifolds and furthermore map the symmetries of these manifolds to each other.
Bergshoeff Eric
Cucu Sorin
Gheerardyn Jos
Proeyen Antoine Van
Vandoren Stefan
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