The anti-de Sitter/conformal field theory (AdS/CFT) correspondence is a remarkable tool for analytically studying strongly coupled physics. Thanks to the AdS/CFT correspondence, strongly correlated quantum systems can be understood as weakly coupled gravity theories, which live in a holographic spacetime with an extra emergent dimension and constant negative curvature. Fundamental observables such as correlation functions are identified with scattering amplitudes in curved spacetime, which, in principle, can be computed by using standard perturbation theory. Unfortunately, such holographic calculations are notoriously difficult, even for tree-level processes involving four external particles. Despite relentless efforts over the past two decades, a full solution to this problem was not found. In this article, we introduce a powerful new method that solves this long-standing problem. We give a closed-form formula for all such four-point functions in a class of theories that constitute the best-known paradigms of AdS/CFT. These models exhaust the theories compatible with maximal supersymmetry, and they live in three, four, and six dimensions. Pivotal to our construction is the use of symmetries. We show that in a judiciously chosen limit, symmetry principles dictate a drastic simplification in holographic correlators, allowing them to be directly computed. Having solved this limit, we further show that the full correlators can be recovered from this special configuration by using only symmetries. In addition to providing valuable explicit expressions that have a wide range of applications in AdS/CFT, our analysis leads to several important conceptual lessons. Our results point out remarkable simplicities underlying the holographic correlators, as well as concrete ways to search for such structures. Moreover, our construction identifies previously unknown elegant underlying organizing principles for holographic correlators. These qualitative features of holographic correlators also echo the exciting progress in the scattering amplitude program in flat space, suggesting tantalizing prospects of future cross-fertilization of ideas.

中文翻译：

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所有最大超对称CFT中的所有全息四点函数

Anti-de Sitter /共形场理论（AdS / CFT）对应关系是用于分析研究强耦合物理学的出色工具。得益于AdS / CFT对应关系，强相关的量子系统可以理解为弱耦合重力理论，它们生活在全息时空中，具有额外的出射尺寸和恒定的负曲率。相关函数之类​​的基本可观测对象通过弯曲时空中的散射幅度来识别，原则上可以通过使用标准摄动理论来计算这些散射幅度。不幸的是，即使对于涉及四个外部粒子的树级过程，这样的全息计算也非常困难。尽管在过去的二十年中付出了不懈的努力，但仍未找到解决该问题的完整解决方案。在本文中，我们推出了一种功能强大的新方法来解决这一长期存在的问题。我们在构成AdS / CFT最著名范例的一类理论中为所有这些四点函数提供了一个封闭形式的公式。这些模型用尽了与最大超对称性兼容的理论，并且存在于三个，四个和六个维度中。使用对称是我们构造的关键。我们表明，在明智选择的范围内，对称性原则要求全息相关器得到极大简化，从而可以直接对其进行计算。解决了这个限制之后，我们进一步证明，仅使用对称性，就可以从这种特殊配置中恢复完整的相关器。除了提供在AdS / CFT中具有广泛应用的有价值的显式表达式外，我们的分析引出了几个重要的概念课。我们的结果指出了全息相关器的显着简化，以及搜索此类结构的具体方法。此外，我们的构造为全息相关器确定了以前未知的优雅基础组织原理。全息相关器的这些定性特征也呼应了平坦空间中散射幅度程序令人兴奋的进展，这暗示了未来跨学科思想的诱人前景。