AI 中文总结
本文基于 Okuda 和 Penedones 的开创性工作，将 AdS₅×S⁵ 弦振幅与 N=4 SYM 关联函数的对偶关系扩展，证明无限 't Hooft 耦合极限下 N=4 SYM 可定义 Carroll CFT，并给出构建 Carroll 关联函数的方法。
AI 中文摘要
在 Okuda 和 Penedones（OP）的开创性论文中，他们提出了关于渐近平直时空（AFS）全息理论的有趣构想：他们证明了 AdS$_5 \times S^5$ 中 4 点玻色子树级弦振幅的平直空间极限，与四维（4d）$\boldsymbol{\mathcal{N} = 4}$ 超杨-米尔斯（SYM）理论中 4 点关联函数的特定双标度极限是对偶的。本文中，我们证明所得的边界关联函数可用于在未来类光无穷远上定义四维 Carroll 共形场论（CFT），这一过程通过将 SYM 中的双标度关联函数映射到 AFS 的共形边界——类光无穷远来实现，Carroll CFT 由此在 $\boldsymbol{\mathcal{N} = 4}$ SYM 的无限 't Hooft 耦合极限中涌现。我们将 OP 的分析扩展到更高点函数，证明平直空间振幅上的 Gram 条件如何对 SYM 关联函数的双标度极限施加约束；随后利用伸缩子弦振幅的软因子化定理，写出双标度极限下 $\boldsymbol{\frac{1}{2}}$-BPS 区的 $\boldsymbol{\mathcal{N} = 4}$ SYM 的递推关系；最后证明这类双标度极限的核心思想可作为工具，通过非引力有效场论的平直空间振幅的特定积分变换，构建一类 Carroll 关联函数，进而定义 Carroll CFT。
英文摘要
In their seminal paper, Okuda and Penedones (OP) put forward an intriguing proposal towards holography in asymptotically flat spacetimes (AFS). They showed that the flat space limit of 4 point bosonic tree-level string amplitude in AdS$_{5}\, \times\, S^{5}$ is dual to a specific double scaling limit of 4 point correlator in four dimensional (4d) $\mathcal{N} = 4$ super Yang-Mills (SYM) theory. In this paper, we show that the resulting boundary correlators can be used to define a 4d Carrollian conformal field theory (CFT) on future null infinity. This is done by mapping the set of doubly scaled correlators in SYM to null infinity, the conformal boundary of AFS. A Carroll CFT thus emerges in the infinite 't Hooft coupling limit of $\mathcal{N} = 4$ SYM. We extend the OP analysis to higher point functions and show how the Gram conditions on flat space amplitude put constraints on the double scaling limit of SYM correlators. We then use the soft factorization theorem for dilatonic string amplitude to write a recursion relation for the $({1}/{2})$-BPS sector of $\mathcal{N} = 4$ SYM in the double scaling limit. Finally, we show that the essential ideas underlying such a double scaling limit can be used as a tool-kit to build a class of Carrollian correlators, and hence define a Carrollian CFT, via certain integral transforms of flat space amplitudes of non-gravitational effective field theories.
Comments46 pages, 1 figure; v2: revised abstract, minor typos
