Abstract
We give a complete proof of the equivalence between constraint equations and field equations for thed=10,N=1 supersymmetric Yang-Mills theory, a result proposed and partially proved recently by Witten [1]. Our approach explicitly reconstructs the superconnection satisfying the constraints from the on shell component fields. A key ingredient of the method is the choice of a suitable family of gauges, effectively eliminating all gauge dependence on anti-commuting co-ordinates. As a corollary, obtained by dimensional reduction, we also deduce the equivalence of constraints and field equations for thed=4,N=4 theory, as well as ford=6,N=2.
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Communicated by A. Jaffe
Research supported in part by the National Science and Engineering Research Council of Canada and the Israel Ministry of Science
On leave of absence from: Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken NJ 07030, USA
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Harnad, J., Shnider, S. Constraints and field equations for ten dimensional super Yang-Mills theory. Commun.Math. Phys. 106, 183–199 (1986). https://doi.org/10.1007/BF01454971
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DOI: https://doi.org/10.1007/BF01454971