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

摘要

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 forthe determination of the holomorphic prepotential characterizing the specialgeometry of these manifolds and necessary in the superconformal tensor calculusof N=2 supergravity. It is demonstrated that there exists certain embeddingsfor which the homogeneous prepotential does not exist. Whether a holomorphicfunction exists or not, the dependence of the gauge kinetic terms on thescalars characterizing these coset in N=2 supergravity theory can be determinedfrom the knowledge of the corresponding embedding, \`a la Gaillard and Zumino.Our results are used to study some of the duality symmetries of heteroticcompactifications of orbifolds with Wilson lines.