Open AccessSpecial geometry of euclidean supersymmetry II. Hypermultiplets and thec-map
Author(s) -
Vicente Cortés,
C. Mayer,
Thomas Mohaupt,
Frank Saueressig
Publication year - 2005
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2005/06/025
Subject(s) - multiplet , euclidean geometry , manifold (fluid mechanics) , cotangent bundle , supersymmetry , physics , affine space , kähler manifold , dimensional reduction , metric (unit) , affine transformation , euclidean space , dimension (graph theory) , mathematical physics , mathematics , pure mathematics , geometry , trigonometric functions , quantum mechanics , mechanical engineering , operations management , engineering , economics , spectral line
We construct two new versions of the c-map which allow us to obtain thetarget manifolds of hypermultiplets in Euclidean theories with rigid N =2supersymmetry. While the Minkowskian para-c-map is obtained by dimensionalreduction of the Minkowskian vector multiplet lagrangian over time, theEuclidean para-c-map corresponds to the dimensional reduction of the Euclideanvector multiplet lagrangian. In both cases the resulting hypermultiplet targetspaces are para-hyper-Kahler manifolds. We review and prove the relevantresults of para-complex and para-hypercomplex geometry. In particular, we givea second, purely geometrical construction of both c-maps, by proving that thecotangent bundle N=T^*M of any affine special (para-)Kahler manifold M ispara-hyper-Kahler.Comment: 36 pages, 1 figur
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