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We consider the loop equation in four-dimensional N=4 SYM, which is afunctional differential equation for the Wilson loop W(C) and expresses thepropagation and the interaction of the string C. Our W(C) consists of thescalar and the gaugino fields as well as the gauge field. The loop C isspecified by six bosonic coordinates y^i(s) and two fermionic coordinates\zeta(s) and \eta(s) besides the four-dimensional spacetime coordinatesx^\mu(s). We have successfully determined, to quadratic order in \zeta and\eta, the parameters in W(C) and the loop differential operator so that theequation of motion of SYM can be correctly reproduced to give the non-linearterm of W(C). We extract the most singular and linear part of our loop equationand compare it with the Hamiltonian constraint of the string propagating onAdS_5 \times S^5 background.Comment: 35 pages, no figures, v2: references adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Loop equation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>super Yang-Mills theory and string field equation on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>AdS</mml:mi><mml:mn>5</mml:mn></mml:…

Loop equation inD=4,N=4super Yang-Mills theory and string field equation onAdS5