Expressions for the generating function of the Donaldson invariants for CP²
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166327062-MIT.pdf
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Author(s)
Malmendier, Andreas
Advisor(s)
Isadore M. Singer.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
The Donaldson invariants for CP2 were obtained as the u-plane integral from a N = 2 supersymmetric topological U(1)-gauge theory by Moore and Witten. We derive the generating function for the Donaldson invariants of CP2 as the stationary phase approximation of the low-energy effective U(I)-gauge theory on CP2 thus obtaining an interpretation of the u-plane integral in terms of determinant line bundles. For the product of the determinant line bundles, the local and global anomalies vanish. Moreover, the product has a canonical trivialization. We show that the u-plane integral also arises as the stationary phase approximation of a heterotic o-model on an elliptic curve at the boundary of the Coulomb branch with the target space CP1 x U(1). The semi-classical generating function is described in terms of determinant line bundles on the Coulomb branch. We show that in terms of the partition function on the elliptic curve, the blow-up function for the Donaldson invariants derived by Fintushel and Stern arises in a natural way.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 161-168).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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