Loop Equation in D=4, N=4 SYM and String Field Equation on AdS₅ × S⁵

الأصل · EN

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 ζand 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 non-linear 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 AdS₅ × S⁵ background.