Supersymmetric. sigma. -models and quaternionic geometry
Our dissertation deals with various topics in supersymmetric {sigma}-models. Chapter I is a brief introduction describing results presented in the next chapters. In Chapter II we analyze classical and quantum properties of a {sigma}-model for which the target space is a real Grassmanian of 2-planes in N-dimensional Euclidean space. We show its analogies to well known CP(N - 1) model. In Chapter III we discuss {sigma}-models on quaternionic Kaehler manifolds which describe matter couplings in N = 2 supergravity theory. We give a local construction of metrics that in the scalar curvature going to zero limit (a global N = 2 supersymmetry limit) give known examples of hyperKaehler metrics. In Chapter IV we develop a geometrical picture of our method which allows for a complete understanding of global properties of the new metrics. It is a non-abelian generalization of the hyperKaehler quotient. We give an orbifold description of these metrics. Chapter V gives rigorous proofs of various statements and assertions presented earlier together with further, more detailed analysis of quaternionic orbifolds. Finally, in Chapter VI, we use our construction in non-compact case to obtain new matter couplings N = 2 supergravity. We construct new non-compact, non-symmetric and complete examples of quaternionic Kaehler manifolds with negative scalar curvature.
- Research Organization:
- State Univ. of New York, Stony Brook, NY (USA)
- OSTI ID:
- 5011043
- Country of Publication:
- United States
- Language:
- English
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