Symplectic Embeddings and Special Kahler Geometry of CP(n-1,1)

Abstract

The embedding of the isometry group of the coset spaces SU(1,n)/ U(1)xSU(n) in Sp(2n+2,R) is discussed. The knowledge of such embedding provides a tool for the determination of the holomorphic prepotential characterizing the special geometry of these manifolds and necessary in the superconformal tensor calculus of N=2 supergravity. It is demonstrated that there exists certain embeddings for which the homogeneous prepotential does not exist. Whether a holomorphic function exists or not, the dependence of the gauge kinetic terms on the scalars characterizing these coset in N=2 supergravity theory can be determined from the knowledge of the corresponding embedding, à la Gaillard and Zumino. Our results are used to study some of the duality symmetries of heterotic compactifications of orbifolds with Wilson lines.

arXiv comment30 pages, TeX, no figures

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• Symplectically invariant flow equations for N=2, D=4 gauged supergravity with hypermultiplets
• Duality invariance in Fayet-Iliopoulos gauged supergravity
• Partial Breaking in Rigid Limit of $\mathcal{N}=2$ Gauged Supergravity