Loop Equation in D = 4 , N = 4 SYM and String Field Equation on AdS 5 × S 5
نویسندگان
چکیده
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 y(s) and two fermionic coordinates ζ(s) and η(s) besides the four-dimensional spacetime coordinates x(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 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 × S background. [email protected] [email protected]
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