论事物的形状：从全息术到弹性
On the Shape of Things: From holography to elastica
摘要：
我们探讨的问题，其中形状的流形是被迫采取时，沉浸在另一个，它必须是一些功能的极值。我们考虑一个家庭的泛函二次依赖于外部曲率和投影的环境曲率。这些泛函捕获了许多物理设置，从全息到膜和弹性的研究。我们提出了一个详细的推导运动方程，被称为形状方程，特别强调规范的自由度在正常帧的选择问题。我们将这些方程应用于高曲率三维引力场下全息纠缠熵的特殊情况，并发现了新的纠缠曲线类型。特别是，我们讨论的情况下，新的大规模引力，我们表明，非测地线纠缠曲线总是有一个较小的壳值的熵泛函。然后，我们应用这种形式主义的计算的纠缠熵的双对数CFTs。然而，测地线提供了纠缠熵的正确值。然后，我们讨论了这些方程的重要性的背景下，经典的弹性和评论的条款，打破规范不变性。
英文摘要：
We explore the question of which shape a manifold is compelled to take when immersed in another one, provided it must be the extremum of some functional. We consider a family of functionals which depend quadratically on the extrinsic curvatures and on projections of the ambient curvatures. These functionals capture a number of physical setups ranging from holography to the study of membranes and elastica. We present a detailed derivation of the equations of motion, known as the shape equations, placing particular emphasis on the issue of gauge freedom in the choice of normal frame. We apply these equations to the particular case of holographic entanglement entropy for higher curvature three dimensional gravity and find new classes of entangling curves. In particular, we discuss the case of New Massive Gravity where we show that non-geodesic entangling curves have always a smaller on-shell value of the entropy functional. Then we apply this formalism to the computation of the entanglement entropy for dual logarithmic CFTs. Nevertheless, the correct value for the entanglement entropy is provided by geodesics. Then, we discuss the importance of these equations in the context of classical elastica and comment on terms that break gauge invariance.
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