Loop equation in D=4, N=4 super Yang-Mills theory and string field equation on AdS5xS5

We consider the loop equation in four-dimensional N=4 SYM, which is a functional differential equation for the Wilson loop W(C) and expresses the propagation and the interaction of the string C. Our W(C) consists of the scalar and the gaugino fields as well as the gauge field. The loop C is specified by six bosonic coordinates yi(s) and two fermionic coordinates ζ(s) and η(s) besides the four-dimensional spacetime coordinates xμ(s). We have successfully determined, to quadratic order in ζ and η, the parameters in W(C) and the loop differential operator so that the equation of motion of SYM can be correctly reproduced to give the nonlinear term of W(C). We extract the most singular and linear part of our loop equation and compare it with the Hamiltonian constraint of the string propagating on AdS5xS5 background