2005/10/28 by Hiroyuki Hata, Akitsugu Miwa
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Geometry #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Scalar (mathematics) #String (physics) #hep-th
paper · pdf · doi:10.1103/physrevd.73.046001
published as Phys.Rev. D73 (2006) 046001 · 35 pages, no figures, v2: references added
arxiv created 2005/10/28 · openalex publication_date 2006/02/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \ensuremathζ(s) and \ensuremathη(s) besides the four-dimensional spacetime coordinates x^\ensuremathμ(s). We have successfully determined, to quadratic order in \ensuremathζ and \ensuremathη, 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 AdS5\ifmmode×\else\texttimes\fiS5 background.