We study the compatibility of the AdS/CFT duality with the bulk and boundary causality, and derive a conformally invariant averaged null energy condition (CANEC) for quantum field theories in 3 and 5-dimensional curved boundaries. This is the generalization of the averaged null energy condition (ANEC) in Minkowski spacetime to curved boundaries, where null energy is averaged along the null line with appropriate weight for conformal invariance. For this purpose we take, as our guiding principle, the no-bulk-shortcut theorem of Gao and Wald, which essentially asserts that when going from one point to another on the boundary, one cannot take a “shortcut through the bulk”. We also discuss the relationship between bulk vs boundary causality and the weak cosmic censorship.

中文翻译：

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来自 AdS/CFT 的共形不变平均空能量条件

我们研究了 AdS/CFT 对偶性与体积和边界因果关系的兼容性，并为 3 维和 5 维弯曲边界中的量子场论推导出了共形不变平均零能量条件 (CANEC)。这是 Minkowski 时空中的平均零能量条件 (ANEC) 到弯曲边界的推广，其中零能量沿零线平均，并具有适当的保形不变性权重。为此，我们将 Gao 和 Wald 的 no-bulk-shortcut 定理作为我们的指导原则，该定理本质上断言，当在边界上从一个点到另一个点时，不能走“通过bulk 的捷径”。我们还讨论了批量与边界因果关系与弱宇宙审查之间的关系。