AI 中文总结
该研究构建了四维 CFT Wightman 关联函数的实 twistor 空间表述，求解了 ambitwistor 变量下的关联函数，建立了与 Grassmannian 关联函数的联系，构造了有质量 twistors 并通过 Penrose 变换重现正确关联函数。
AI 中文摘要
我们建立了四维共形场论（CFT$_4$）Wightman 关联函数的实 twistor 空间表述，在 ambitwistor 空间中写出共形生成元与小群约束，二次条件 $Z\cdot W=0$ 自然源自小群约束。随后我们用 ambitwistor 变量求解了宇称偶和宇称奇关联函数，还通过半傅里叶变换建立了 ambitwistor 关联函数与螺旋度基 Grassmannian 中关联函数的联系，并发展了 Penrose 变换以恢复对应的位置空间关联函数。我们注意到，对于含多个张量结构的关联函数，Penrose 变换会产生共形不变结构的完整空间，但对相关 Schwinger 积分进行正则化会选出物理关联函数。最后，从协变 Grassmannian 表述出发，我们构造了有质量 twistors，使其小群对称性明显，并发展了它们的 Penrose 变换，该变换同样能重现正确的位置空间关联函数。
英文摘要
We develop a real twistor-space formulation of four-dimensional CFT Wightman correlators. We write the conformal generators and little-group constraints in ambitwistor space. The quadric condition $Z\cdot W$=0 arises naturally from the little-group constraints. We then solve for both the parity-even and parity-odd correlators in the ambitwistor variables. We further establish the connection between the ambitwistor correlators and the ones in the helicity-basis Grassmannian via a half-Fourier transform, and also develop the Penrose transform to recover the corresponding position-space correlators. We notice that for correlators with multiple tensor structures, the Penrose transform yields the full space of conformally invariant structures, but regularizing the associated Schwinger integrals selects the physical correlator. Finally, starting from the covariant Grassmannian formulation, we construct massive twistors that make the little-group symmetries manifest and develop their Penrose transform, which again reproduces the correct position-space correlators.
Comments33 pages main text, 6 pages appendix. Comments are welcome
