Towards a general fluid/gravity correspondence
Towards a general fluid/gravity correspondence
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DOI：
10.1103/physrevd.91.044001
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发表时间：
2015-02-02
影响因子：
5
通讯作者：
Taylor, Marika
中科院分区：
文献类型：
--
作者：
Pinzani-Fokeeva, Natalia;Taylor, Marika
我们建立了一般的（d + 2）维度量的建设对应的（d + 1）维流体，全息代表的流体动力学制度的假定的对偶理论。我们给一般种子平衡度量适合通用体应力能量张量，并讨论了共形重新标度的超曲面上定义的流体的影响。然后，我们展示了如何使用相对论梯度展开获得相应的流体力学度量，并讨论所得方程的可积性条件。所得到的流体的应力能张量，在平衡和远离平衡，满足二次约束。我们解释这种约束条件的两种可能的状态方程的流体，并表明，只有一个两个方程是物理的。我们说明了我们的讨论与截止反德西特流体的例子，我们发现在UV共形场理论的变形方面的精确解释。最后，我们讨论了现代流体/重力的方法，本文和早期的膜范式之间的关系。
We set up the construction of generic (d + 2)-dimensional metrics corresponding to (d + 1)-dimensional fluids, representing holographically the hydrodynamic regimes of the putative dual theories. We give general seed equilibrium metrics appropriate to generic bulk stress energy tensors and discuss the implications of conformal rescalings of the hypersurface on which the fluid is defined. We then show how to obtain the corresponding hydrodynamic metrics using a relativistic gradient expansion and discuss the integrability conditions of the resulting equations. The stress energy tensors of the resulting fluids, both at and away from equilibrium, satisfy a quadratic constraint. We interpret this constraint in terms of two possible equations of state for the fluid and show that only one of the two equations is physical. We illustrate our discussions with the example of the cutoff anti-de Sitter fluid, for which we find the precise interpretation in terms of deformations of the UV conformal field theory. Finally we discuss the relation between the modern fluid/gravity approach taken in this paper and the earlier membrane paradigm.