三维$\u003cspan style="font-style: italic; font-family: serif;"\u003eN\u003c/span\u003e$=1 SCFT中守恒超流的三点函数：任意超自旋的一般形式体系
Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
AI总结：
本研究针对三维N=1超共形场论中守恒高自旋超流三点函数，构建显式超对称形式体系，完成s_i≤20的分类并推广至任意超自旋，揭示其结构与超自旋三角不等式的关联。
摘要：
我们分析了三维$\u003cspan style="font-style: italic; font-family: serif;"\u003eN\u003c/span\u003e$=1超共形场论（SCFT）中守恒高自旋超流三点函数的一般结构。研究表明，超对称性对守恒高自旋流的关联函数施加了额外限制。我们发展了一种显式超对称形式体系，用于计算三点函数$\u003cspan style="font-style: italic; font-family: serif;"\u003eJ\u003c/span\u003e_{s_1} \u003cspan style="font-style: italic; font-family: serif;"\u003eJ\u003c/span\u003e'_{s_2} \u003cspan style="font-style: italic; font-family: serif;"\u003eJ\u003c/span\u003e''_{s_3}$，其中$\u003cspan style="font-style: italic; font-family: serif;"\u003eJ\u003c/span\u003e_{s_1}$、$\u003cspan style="font-style: italic; font-family: serif;"\u003eJ\u003c/span\u003e'_{s_2}$和$\u003cspan style="font-style: italic; font-family: serif;"\u003eJ\u003c/span\u003e''_{s_3}$分别是超自旋为$s_1$、$s_2$和$s_3$的守恒高自旋超流（自旋可为整数或半整数）。我们采用仅受计算能力限制的计算方法，解析地施加了由超场守恒方程和超空间点置换对称性带来的约束。文中给出了三点函数的显式解，并对$s_i \u003cspan style="text-decoration: overline;"\u003e≤\u003c/span\u003e 20$的结果进行了完整分类；分类规律十分清晰，我们提出该分类适用于任意超自旋。研究证明，格拉斯曼偶三点函数可由一个宇称偶结构和一个宇称奇结构完全确定，而格拉斯曼奇三点函数仅由一个宇称偶结构确定。格拉斯曼偶关联函数中宇称奇结构的存在性需满足一组关于超自旋的三角不等式。为完整起见，我们还分析了包含守恒高自旋超流与标量超场的三点函数结构。
英文摘要：
We analyse the general structure of the three-point functions of conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-point function $\langle \mathbf{J}^{}_{s_{1}} \mathbf{J}'_{s_{2}} \mathbf{J}''_{s_{3}} \rangle$, where $\mathbf{J}^{}_{s_{1}}$, $\mathbf{J}'_{s_{2}}$ and $\mathbf{J}''_{s_{3}}$ are conserved higher-spin supercurrents with superspins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). Using a computational approach limited only by computer power, we analytically impose the constraints arising from the superfield conservation equations and symmetries under permutations of superspace points. Explicit solutions for three-point functions are presented and we provide a complete classification of the results for $s_{i} \leq 20 $; the pattern is very clear, and we propose that our classification holds for arbitrary superspins. We demonstrate that Grassmann-even three-point functions are fixed up to one parity-even structure and one parity-odd structure, while Grassmann-odd three-point functions are fixed up to a single parity-even structure. The existence of the parity-odd structure in the Grassmann-even correlation functions is subject to a set of triangle inequalities in the superspins. For completeness, we also analyse the structure of three-point functions involving conserved higher-spin supercurrents and scalar superfields.
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