Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed viewpoint of field theory and holography. A set of basic methods for the computation is developed and illustrated with simple examples such as free theories and conformal field theories. The structures of the ultraviolet divergences and the universal parts are determined and compared with the holographic descriptions of entanglement entropy. The utility of quantum inequalities of entanglement are discussed and shown to derive the $\mathcal{C}$ theorem that constrains renormalization group flows of quantum field theories in diverse dimensions.

中文翻译：

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纠缠熵：全息和重归一化组

纠缠熵在量子场论中扮演着各种角色，包括通过全息原理实现的量子态与引力之间的联系。本文从场论和全息学的混合观点对纠缠熵进行了综述。开发了一组基本的计算方法，并通过简单的示例（例如自由理论和保形场理论）进行了说明。确定紫外线发散和通用部分的结构，并将其与纠缠熵的全息描述进行比较。讨论了纠缠量子不等式的效用，并证明了得出$\mathcal{C}$ 约束量子场论在不同维度上重归一化群流的定理。