We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their dual description in terms of periodic Wilson loops. A form factor is decomposed into a sequence of known pentagon transitions and a new universal object that we call the “form factor transition.” This transition is subject to a set of nontrivial bootstrap constraints, which are sufficient to fully determine it. We evaluate the form factor transition for maximally helicity-violating form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce operator product expansion predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature.

中文翻译：

---

运营商产品扩展的外形尺寸

我们建议针对当地运营商的平面形状因子扩展运营商产品 $\mathcal{ñ}=4$SYM理论。这种扩展基于这些对象的双重共形对称性，或者等效地，基于周期性Wilson环，它们的双重描述的共形对称性。形状因数分解为一系列已知的五边形过渡和一个新的通用对象，我们称其为“形状因数过渡”。此过渡受一组非平凡的引导约束，这些约束足以完全确定它。我们在扰动理论中对应力张量超多手征的手性一半的最大违反螺旋性的形状因子进行了形式转换，并在任何循环顺序下将其用于生成算子乘积展开预测。我们将单环和双环预测与文献中可用的数据进行匹配。