Lecture notes on holographic renormalization
Lecture notes on holographic renormalization
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DOI：
10.1088/0264-9381/19/22/306
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发表时间：
2002-09
影响因子：
3.5
通讯作者：
Kostas Skenderis
中科院分区：
文献类型：
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作者：
Kostas Skenderis
我们回顾全息重正化的形式主义。我们首先讨论渐近反德西特（AdS）时空的数学结果。然后我们概述全息重整化的一般方法。通过在一个简单的例子中处理所有细节来说明该方法：反德西特时空中的巨大标量场。讨论包括壳上重整化作用、全息 Ward 恒等式、异常和重整化群 (RG) 方程的推导，以及重整化一点、两点和四点函数的计算。然后我们讨论该方法在全息 RG 流中的应用。我们还表明，渐近 AdS 时空的近边界分析结果可以分析地继续应用于渐近德西特时空。特别是，结果表明，德西特时空的布朗-约克应力能张量与相关 AdS 时空的布朗-约克应力能张量相等，直到有维度相关的符号。
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, holographic Ward identities, anomalies and renormalization group (RG) equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown–York stress energy tensor of de Sitter spacetime is equal, up to a dimension-dependent sign, to the Brown–York stress energy tensor of an associated AdS spacetime.