Reconstruction of superconnection from physical fields in the N=4 supersymmetric Yang-Mills theory

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Abstract
The authors present a method for reconstructing a superconnection in the N=3 superspace formulation of the N=4 SYM theory in terms of on-shell physical fields in Minkowski space. This is done through the formulation of N=3 constraint equations in terms of superdifferential forms. In this formulation the constraints imply an overdetermined system of differential equations on anticommuting variables for which the Frobenius consistency conditions are not satisfied globally, but are satisfied only on submanifolds parametrised by solutions of dynamical equations of motion in Minkowski space for the N=4 SYM theory.