Elliptic Yang–Mills flow theory |
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Authors: | Rémi Janner Jan Swoboda |
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Affiliation: | 1. +41 41 249 58 96;2. Centralschweizerische Kraftwerke AG, 6032 Emmen, Switzerland;3. Mathematisches Institut der Universit?t München, 80333 München, Germany |
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Abstract: | We lay the foundations of a Morse homology on the space of connections on a principal G‐bundle over a compact manifold Y, based on a newly defined gauge‐invariant functional on . While the critical points of correspond to Yang–Mills connections on P, its L2‐gradient gives rise to a novel system of elliptic equations. This contrasts previous approaches to a study of the Yang–Mills functional via a parabolic gradient flow. We carry out the analytical details of our programme in the case of a compact two‐dimensional base manifold Y. We furthermore discuss its relation to the well‐developed parabolic Morse homology over closed surfaces. Finally, an application of our elliptic theory is given to three‐dimensional product manifolds . |
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Keywords: | Yang– Mills functional Morse homology nonlinear Cauchy‐Riemann equation spectral flow 58E15 58J30,35R01 |
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