Dyson–Schwinger equations and $$\mathcal{N}=4$$ N = 4 SYM in Landau gauge

$$\mathcal{N}=4$$ 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 and the 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 discuss which role the Gribov–Singer ambiguity in this context could play, should it exist in this theory.