Holomorphic vector bundles, knots and the Rozansky-Witten invariants
Feb, 200021 pages
Published in:
- Adv.Theor.Math.Phys. 5 (2002) 457-481
e-Print:
- hep-th/0002168 [hep-th]
Report number:
- IC-2000-9
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Abstract:
Link invariants, for 3-manifolds, are defined in the context of the Rozansky-Witten theory. To each knot in the link one associates a holomorphic bundle over a holomorphic symplectic manifold X. The invariants are evaluated for b_{1}(M) \geq 1 and X Hyper-Kaehler. To obtain invariants of Hyper-Kaehler X one finds that the holomorphic vector bundles must be hyper-holomorphic. This condition is derived and explained. Some results for X not Hyper-Kaehler are presented.- gauge field theory: Yang-Mills
- Chern-Simons term
- fibre bundle
- differential geometry: symplectic
- knot theory
- differential forms
- analytic properties
- charge: topological
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