受保护的且具有一致超越性的
Protected and uniformly transcendental
AI总结：
本研究证明${\frak N}=4$ SYM中受保护双标量算符的两点函数在三环阶内具有一致超越度，推测该性质适用于全微扰级数并预测全圈阶领头ε修正，还发现三点函数软极限与两点函数的微扰关系并外推至全圈阶。
摘要：
我们证明，在维数正规化下计算的${\frak N}=4$ SYM中受保护双标量算符的两点函数，在三环阶内呈现出一致的超越度。我们推测这一性质对整个微扰级数都成立，并利用显式结果提出了对所有圈阶的领头阶ε修正的预测。我们还研究了动量空间中这类算符的三点函数的软极限，指出了其与两点函数之间一种简单且出人意料的微扰关系，并将该关系外推至所有圈阶。
英文摘要：
We show that the two-point function of protected bi-scalar operators in ${\cal N}=4$ SYM evaluated in dimensional regularization exhibits a uniform degree of transcendentality 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.
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