Schwinger-Dyson and Large $N_{c}$ Loop Equation for Supersymmetric Yang-Mills Theory

TL;DR

This paper derives an infinite set of Schwinger-Dyson equations for N=1 supersymmetric Yang-Mills theory using Wilson loops in superspace, leading to a closed loop equation in the large N_c limit.

Contribution

It introduces a novel approach to formulate Schwinger-Dyson equations for supersymmetric gauge theories using superspace Wilson loops, simplifying the analysis in the large N_c limit.

Findings

Derived an infinite sequence of Schwinger-Dyson equations for N=1 SYM.

Formulated a closed loop equation for the Wilson-loop average in the large N_c limit.

Abstract

We derive an infinite sequence of Schwinger-Dyson equations for $N=1$ supersymmetric Yang-Mills theory. The fundamental and the only variable employed is the Wilson-loop geometrically represented in $N=1$ superspace: it organizes an infinite number of supersymmetrizing insertions into the ordinary Wilson-loop as a single entity. In the large $N_{c}$ limit, our equation becomes a closed loop equation for the one-point function of the Wilson-loop average.