Holonomy groups,complex structures andD=4 topological Yang-Mills theory |
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Authors: | A Galperin O Ogievetsky |
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Institution: | 1. Laboratory of Theoretical Physics, JINR, P.O. Box 79, SU-101000, Moscow, USSR 3. Institute for Theoretical Physics, University Karlsruhe, Kaiserstra?e 12, W-7500, Karlsruhe 1, Federal Republic of Germany
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Abstract: | We study conditions for the existence of extended supersymmetry in topological Yang-Mills theory. These conditions are most conveniently formulated in terms of the holonomy group of the underlying manifold, on which the topological Yang-Mills theory is defined. For irreducible manifolds we find that extended supersymmetries are in 1–1 correspondence with covariantly constant complex structures. Therefore, the topological Yang-Mills theory on any Kähler manifold possesses one additional supersymmetry and on any hyper Kähler manifold there are three additional supersymmetries. The Donaldson map, which plays a crucial role in the construction of the topological invariants, is generalized for Kähler manifolds, thus providing candidates for new invariants of complex manifolds. |
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