论文标题
在弯曲背景下，在一般状态下的CFT的形式主义嵌入形式主义
An embedding formalism for CFTs in general states on curved backgrounds
论文作者
论文摘要
我们基于Fefferman和Graham的环境指标，将嵌入空间形式主义的嵌入式形式形式概括为在非平凡状态和弯曲背景上的形式。环境度量标准是$ d+2 $尺寸的洛伦兹ricci-flat度量，并取代了嵌入式空间的Minkowski度量。它在规范上与$ d $维二维的共形流形相关联，这是cft $ {} _ d $ live的物理时空。我们建议使用环境空间的适当几何不变式作为构建块的构造CFT $ {} _ d $ $ n $ - 点功能，并在弯曲的背景下进行弯曲背景。这至少在全息CFT中捕获了多压力 - 能量张量的非变化1分函数的贡献。我们将形式主义应用于热CFT的2分函数，与全息计算的确切一致性和基于热算子产品扩展（OPES）的期望以及在未知的现有方法的挤压球体上的CFT，并表明该方法的实用性。
We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat metric in $d+2$ dimensions and replaces the Minkowski metric of the embedding space. It is canonically associated with a $d$-dimensional conformal manifold, which is the physical spacetime where the CFT${}_d$ lives. We propose a construction of CFT${}_d$ $n$-point functions in non-trivial states and on curved backgrounds using appropriate geometric invariants of the ambient space as building blocks. This captures the contributions of non-vanishing 1-point functions of multi-stress-energy tensors, at least in holographic CFTs. We apply the formalism to 2-point functions of thermal CFT, finding exact agreement with a holographic computation and expectations based on thermal operator product expansions (OPEs), and to CFTs on squashed spheres where no prior results are known and existing methods are difficult to apply, demonstrating the utility of the method.
