Gauge fields -strings duality and the loop equation

We explore gauge fields - strings duality by means of the loop equations andthe zigzag symmetry. The results are striking and incomplete. Striking -because we find that the string ansatz proposed in [A.M. Polyakov,hep-th/9711002] satisfies gauge theory Schwinger-Dyson equations precisely atthe critical dimension D=4. Incomplete - since we get these results only in theWKB approximation and only for a special class of contours. The ways to gobeyond these limitations and in particular the OPE for operators defined on theloop are also discussed