A general framework for gravitational charges and holographic renormalization
A general framework for gravitational charges and holographic renormalization
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DOI：
10.1142/s0217751x22501056
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发表时间：
2021-11
影响因子：
1.6
通讯作者：
V. Chandrasekaran;E. Flanagan;I. Shehzad;A. Speranza
中科院分区：
文献类型：
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作者：
V. Chandrasekaran;E. Flanagan;I. Shehzad;A. Speranza
利用协变相空间技术，我们发展了一个构造引力理论中与微分同胚有关的电荷的一般框架。这个框架既包括与时空分区域相关的局域电荷，也包括整个时空的全球守恒电荷。电荷的表达式包括分区作用中边界项和角项的贡献，并通过诉诸分区的变分原理使其变得明确，该原理选择了通过边界的辛通量的首选形式。子区域相空间上电荷的泊松括号重现了开放子系统的Barnich和Troesshelt的括号，从而从第一原理给出了这个括号的一种新的推导。在渐近边界的背景下，我们证明了一旦找到合适的反项来保证有限的作用量，全息重整化过程总是可以用来获得有限的电荷和通量。这使得通过放松施加在无穷远处的边界条件来研究更大的渐近对称群成为可能。我们进一步给出了一个显式计算作用量和辛势的反项的算法，并作为我们框架的一个应用，证明了它重现了广义Bondi-Metzner-Sachs代数的电荷的已知表达式。电子邮件：venchandrasekaran@ias.edu eef3@cornell.edu is 354@cornell.edu asperanz@gmail.com
We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques. This framework encompasses both localized charges associated with spacetime subregions, as well as global conserved charges of the full spacetime. Expressions for the charges include contributions from the boundary and corner terms in the subregion action, and are rendered unambiguous by appealing to the variational principle for the subregion, which selects a preferred form of the symplectic flux through the boundaries. The Poisson brackets of the charges on the subregion phase space are shown to reproduce the bracket of Barnich and Troessaert for open subsystems, thereby giving a novel derivation of this bracket from first principles. In the context of asymptotic boundaries, we show that the procedure of holographic renormalization can be always applied to obtain finite charges and fluxes once suitable counterterms have been found to ensure a finite action. This enables the study of larger asymptotic symmetry groups by loosening the boundary conditions imposed at infinity. We further present an algorithm for explicitly computing the counterterms that renormalize the action and symplectic potential, and, as an application of our framework, demonstrate that it reproduces known expressions for the charges of the generalized Bondi-Metzner-Sachs algebra. venchandrasekaran@ias.edu eef3@cornell.edu is354@cornell.edu asperanz@gmail.com