Schwinger-Dyson Equation for Supersymmetric Yang-Mills Theory

TL;DR

This paper derives a supersymmetric form of the Schwinger-Dyson and loop equations for 4D supersymmetric Yang-Mills theory, solves them perturbatively, and explores implications for string dynamics.

Contribution

It introduces a new manifestly supersymmetric and supergauge invariant formulation of loop equations in supersymmetric Yang-Mills theory, extending the abelian case.

Findings

Derived a supersymmetric loop equation in superspace

Solved the equation at leading order in perturbation theory

Explicitly performed one-loop renormalization of Wilson-loop average

Abstract

We study our Schwinger-Dyson equation as well as the large $N_{c}$ loop equation for supersymmetric Yang-Mills theory in four dimensions by the N=1 superspace Wilson-loop variable. We are successful in deriving a new manifestly supersymmetric form in which a loop splitting and joining are represented by a manifestly supersymmetric as well as supergauge invariant operation in superspace. This is found to be a natural extension from the abelian case. We solve the equation to leading order in perturbation theory or equivalently in the linearized approximation, obtaining a desirable nontrivial answer. The super Wilson-loop variable can be represented as the system of one-dimensional fermion along the loop coupled minimally to the original theory. One-loop renormalization of the one-point Wilson-loop average is explicitly carried out, exploiting this property. The picture of string dynamics obtained is briefly discussed.