Title: Exploring Structure Constants in Planar $\mathcal{N} = 4$ SYM: From Small Spin to Strong Coupling Show Chinese title

Title: 探索平面$\mathcal{N} = 4$ SYM 中的结构常数：从小自旋到强耦合

Abstract: We study the structure constants of two conformal primary operators and one spinning operator in planar $\mathcal{N} = 4$ Super-Yang-Mills theory using the hexagon formalism. By analytically continuing in the spin, we derive a formula for computing these structure constants at any coupling in the small-spin limit, up to a normalization factor. This formula allows us to explore their analytical properties at strong coupling. In this regime, using classical string calculations and a suitable ansatz, we extend our analysis to finite-spin operators, verifying recent two-loop results for structure constants in string theory and generalizing them to operators with arbitrary R-charges. Show Chinese abstract

Abstract: 我们使用六边形形式主义研究平面$\mathcal{N} = 4$超杨-米尔斯理论中两个共形原初算符和一个自旋算符的结构常数。 通过在自旋上进行解析延拓，我们推导出一个公式，用于计算小自旋极限下任意耦合的这些结构常数，除了一个归一化因子。 该公式使我们能够探索它们在强耦合下的解析性质。 在这个区域内，利用经典弦计算和合适的假设，我们将分析扩展到有限自旋算符，验证了最近关于弦理论中结构常数的两环结果，并将其推广到具有任意 R 电荷的算符。