A Matrix String Interpretation of the Large N Loop Equation

The existence two S-dual descriptions of (N,1) string bound states suggests that the strong coupling behaviour of electric flux lines in large N 2D SYM theory has a dual description in terms of weakly coupled IIB string theory. In support of this identification, we propose a dual interpretation of the SYM loop equation as a perturbative string Ward identity, expressing the conformal invariance of the corresponding boundary interaction. This correspondence can be viewed as a weak coupling check of the matrix string conjecture. Introduction Consider the large N limit of 1+1-dimensional N = 8 supersymmetric Yang-Mills theory with gauge group U(N), described by the Lagrangian (here and in most of this paper we omit all fermionic fields) S = ∫ dX tr [ 1 g2 YM F 2 αβ + (DαΦ ) − g YM [Φ,Φ] ] . (1) with i = 2, . . . , 9. This model can be viewed as the dimensional reduction of ten dimensional N = 1 SYM theory, where Φ represent the 8 transverse components of the ten-dimensional gauge potential Aμ. We will be interested in giving a string interpretation of the loop equation of motion [1, 2] of the Wilson loop average W [X] = 〈