Dyson-Schwinger equations and ${\cal N}=4$ SYM in Landau gauge

TL;DR

This paper explores Dyson-Schwinger equations in ${\cal N}=4$ Super Yang-Mills theory within Landau gauge, aiming to understand non-perturbative aspects and the impact of gauge ambiguities, revealing a conformal solution similar to ordinary Yang-Mills theories.

Contribution

It derives Dyson-Schwinger equations for ${\cal N}=4$ SYM in Landau gauge and identifies a conformal solution, providing insights into gauge fixing ambiguities and non-perturbative structure.

Findings

Found a conformal solution in Landau gauge approximation.

Identified potential role of Gribov-Singer ambiguity.

Resembles features of ordinary Yang-Mills theories.

Abstract

${\cal N}=4$ Super Yang-Mills theory is a highly constrained theory, and therefore a valuable tool to test the understanding of less constrained Yang-Mills theories. Our aim is to use it to test our understanding of both the Landau gauge beyond perturbation theory as well as truncations of Dyson-Schwinger equations in ordinary Yang-Mills theories. We derive the corresponding equations within the usual one-loop truncation for the propagators after imposing the Landau gauge. We find a conformal solution in this approximation, which surprisingly resembles many aspects of ordinary Yang-Mills theories. We furthermore identify which role the Gribov-Singer ambiguity in this context could play, should it exist in this theory.