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arXiv 0907.1156hep-thgr-qchep-ph
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玻尔兹曼与爱因斯坦之间的AdS/CFT联系

An AdS/CFT Connection between Boltzmann and Einstein

Ramakrishnan Iyer, Ayan Mukhopadhyay

备注：
42 pages; this contains exactly the same content as the earlier versions but the presentation has been made more concise and readable; some references which are not directly relevant to this work have been removed at the insistence of PRD referees.
发表信息：
Phys.Rev.D81:086005,2010
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摘要：

AdS/CFT对应将场论中具有普遍强耦合动力学的扇区定义为具有负宇宙学常数的爱因斯坦方程所描述的AdS中纯引力的对偶。在这里，我们从场论的观点解释了这个扇区的动力学是如何由能量-动量张量\emph{alone}的期望值决定的。我们首先表明，玻尔兹曼方程有非常特殊的解决方案，可以\textit{functionally}完全确定的能量动量张量。我们称这些解决方案为\textit{conservative solutions}。我们指出为什么保守的解决方案也应该存在，当我们完善这个动力学描述去更接近精确的微观理论，甚至远离弱耦合的制度，使没有动力学描述可以采用。我们认为这些\textit{conservative solutions}在强耦合和大$N$下形成了与纯引力对偶的普适扇区。在此基础上，我们提出了一个关于能量动量张量的\textit{regularity condition}，使得纯引力中的对偶解具有光滑的未来视界。我们还研究，如果不可逆性只出现在长时间尺度的观察，不像玻尔兹曼方程的情况下。

英文摘要：

The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor \emph{alone}. We first show that the Boltzmann equation has very special solutions which could be \textit{functionally} completely determined in terms of the energy-momentum tensor alone. We call these solutions \textit{conservative solutions}. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these \textit{conservative solutions} form the universal sector dual to pure gravity at strong coupling and large $N$. Based on this observation, we propose a \textit{regularity condition} on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

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