Large $N$ Solution of the 2D Supersymmetric Yang-Mills Theory

TL;DR

This paper solves the Schwinger-Dyson equations for 2D supersymmetric Yang-Mills theory, revealing that planar Wilson loops are described by a Nambu string without folds and demonstrating supersymmetry preservation on the lattice.

Contribution

It provides an exact large N solution for 2D supersymmetric Yang-Mills theory using Schwinger-Dyson equations and explores lattice formulation preserving supersymmetry.

Findings

Planar Wilson loops correspond to a Nambu string without folds.

Supersymmetry remains unbroken on the lattice.

The equations form a closed set when supplemented with supersymmetry constraints.

Abstract

The Schwinger-Dyson equations of the Makeenko-Migdal type, when supplemented with some simple equations as consequence of supersymmetry, form a closed set of equations for Wilson loops and related quantities in the two dimensional super-gauge theory. We solve these equations. It appears that the planar Wilson loops are described by the Nambu string without folds. We also discuss how to put the model on a spatial lattice, where a peculiar gauge is chosen in order to keep one supersymmetry on the lattice. Supersymmetry is unbroken in this theory. We comment on possible generalization of these considerations to other models.