Symplectic embeddings and special Kähler geometry of CP(n − 1, 1) Original Research Article

The embedding of the isometry group of the coset spaces SU(1, n)/[U(1) × SU(n)] in Sp(2n+2, R) is discussed. 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 exist 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 cosets in N = 2 supergravity theory can be determined from the knowledge of the corresponding embedding, á la Gaillard and Zumino. Our results are used to study some of the duality symmetries of heterotic compactifications of orbifolds with Wilson lines.