Loop Equation in D=4, N=4 SYM and String Field Equation on AdS_5 \times S^5

Details Loop Equation in D=4, N=4 SYM and String Field Equation on AdS_5 \times S^5 Loop Equation in D=4, N=4 SYM and String Field Equation on AdS_5 \times S^5

2005-10-18

arxiv.org/abs/hep-th/0510150v2

Phys.Rev. D73 (2006) 046001

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, no figures, v2: references added

Scientific paper

10.1103/PhysRevD.73.046001

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^i(s) and two fermionic coordinates \zeta(s) and \eta(s) besides the four-dimensional spacetime coordinates x^\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 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 AdS_5 \times S^5 background.

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