Gauge fields - strings duality and the loop equation

TL;DR

This paper investigates the gauge fields - strings duality using loop equations and zigzag symmetry, finding that a string ansatz satisfies gauge theory equations in four dimensions within a specific approximation.

Contribution

It demonstrates that a particular string ansatz fulfills gauge theory Schwinger-Dyson equations at D=4, highlighting the duality in a specific approximation and contour class.

Findings

String ansatz satisfies Schwinger-Dyson equations at D=4

Results obtained in WKB approximation

Analysis limited to a special class of contours

Abstract

We explore gauge fields - strings duality by means of the loop equations and the 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 at the critical dimension D=4. Incomplete - since we get these results only in the WKB approximation and only for a special class of contours. The ways to go beyond these limitations and in particular the OPE for operators defined on the loop are also discussed.