AI 中文总结
该研究在辛双格拉斯曼框架下开展CFT$_4$与AdS$_5$的四点函数研究，推导因子化公式、发展扭子空间形式并扩展至$\boldsymbol{\text{N}}=1$超对称，测试于超杨-米尔斯理论并探讨超引力应用。
AI 中文摘要
我们启动了四维共形场论（CFT$_4$）的辛双格拉斯曼框架下四点函数的研究，推导了与散射振幅类似的因子化公式，并自举了多个AdS$_5$交换关联函数的实例，涉及标量、光子、费米子、胶子和引力子。这些关联函数是格拉斯曼矩阵子式的有理函数，相比之下，其动量空间对应物要复杂得多。随后，我们发展了$GL(2,\boldsymbol{\text{R}})$扭子空间形式，推导了彭罗斯变换和扭子格拉斯曼，在其中发现了极其简洁的表达式；我们还找到了其向$\boldsymbol{\text{N}}=1$超对称的优美自然扩展，推导了超对称彭罗斯变换和超扭子格拉斯曼。从扭子空间进行半傅里叶变换，我们推导了对应旋量-螺旋度变量的超对称辛双格拉斯曼。我们在AdS$_5$ $\boldsymbol{\text{N}}=1$超杨-米尔斯理论的背景下测试了这一形式，在其中施加了一致的因子化条件，并输入自举得到的四费米子关联函数，以获得涉及胶子、标量和费米子的关联函数。最后，我们讨论了其在超引力理论中的应用。
英文摘要
We initiate the study of four point functions in the symplectic bi-Grassmannian framework for four dimensional conformal field theories. We derive factorization formulae analogous to those for scattering amplitudes and bootstrap several examples of AdS$_5$ exchange correlation functions involving scalars, photons, fermions, gluons and gravitons. These correlators are rational functions of the minors of the Grassmannian matrices in contrast to their momentum space counterparts which are much more complicated. We then develop the $GL(2,\mathbb{R})$ twistor space formalism, deriving the Penrose transform and the twistorial Grassmannian where we find remarkably simple expressions. We also find an elegant and natural extension to $\mathcal{N}=1$ supersymmetry, deriving the supersymmetric Penrose transform and the super-twistor Grassmannian. Performing a half-Fourier transform from twistor space, we derive the supersymmetric symplectic bi-Grassmannian corresponding to spinor-helicity variables. We test our formalism in the context of AdS$_5$ $\mathcal{N}=1$ super-Yang Mills theory where we impose consistent factorization and input the bootstrapped four-fermion correlator to obtain those involving gluons, scalars and fermions. Finally, we discuss the application to supergravity theories.
Comments37 pages main text+13 pages appendices, 1 table. v2: References added, minor typos corrected
