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.

30 pages, TeX, no figures

References in corpus (2)

• Minimal Higgs Branch for the Breaking of Half of the Supersymmetries in N=2 Supergravity
• SpaceTime Duality And $\frac{SU(n,1)}{SU(n)\otimes U(1)}$ Cosets Of Orbifold Compactification

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