AI 中文总结
该研究利用辅助极化旋量形式和超空间技术，在三维$\mathcal{N}=3,4$超共形场论中构建三点不变结构列表，借助非阿贝尔$R$ - 对称性产生新型不变结构，用于枚举自旋三点关联函数结构形式，明确了守恒算符关联函数的结构特点。
AI 中文摘要
我们使用辅助极化旋量形式和超空间技术，在具有$\mathcal{N}=3$和$\mathcal{N}=4$超共形对称性的三维超共形场论（SCFTs）中，构建完整且最小的三点不变结构列表。$\mathcal{N}=3,4$的非阿贝尔$R$ - 对称性产生了由反对称不变张量构建的新型不变结构。这些不变量用于枚举三维SCFTs中一般以及守恒自旋超场算符的自旋三点关联函数的结构形式。对于守恒算符，我们发现$\mathcal{N}=3$关联函数在一个宇称偶数和一个宇称奇数结构内是固定的，而$\mathcal{N}=4$守恒关联函数允许两个宇称偶数结构和一个宇称奇数结构，第二个宇称偶数结构与镜像对称破缺相关。
英文摘要
We use the auxiliary polarization spinor formalism together with superspace techniques to construct a complete and minimal list of 3-point invariant structures in three-dimensional superconformal field theories (SCFTs) with $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal symmetry. The existence of non-abelian $R$-symmetry for $\mathcal{N}=3,4$ gives rise to novel invariant structures built from the antisymmetric invariant tensor. These invariants are used to enumerate the structural form of spinning 3-point correlators of general as well as conserved spinning superfield operators in 3d SCFTs. For conserved operators, we find that the $\mathcal{N}=3$ correlators are fixed upto one parity-even and one parity-odd structure, while $\mathcal{N}=4$ conserved correlators admit two parity-even structures and one parity-odd structure, with the second parity-even structure associated with mirror symmetry breaking.
Comments31 pages
