Protected and uniformly transcendental - Marco S. Bianchi (Journal of High Energy Physics, 2023)
Abstract We show that the two-point function of protected bi-scalar operators in N $$ \mathcal{N} $$ = 4 SYM evaluated in dimensional regularization exhibits a uniform transcendental weight up to three-loop order. We conjecture that this property holds for the whole perturbative series and leverage the explicit results to postulate a prediction for the leading, order ϵ, correction to all loop orders. We also consider the soft limit of three-point functions of such operators in momentum space and point out a simple and surprising perturbative relation to two-point functions, which we also extrapolate to all loop orders.