arXiv 1209.02602012-09hep-thnucl-th

关于全息剪切粘度与熵密度比的讨论

Comments on the holographic shear viscosity to entropy density ratio

Kiminad A. Mamo

备注：: 9 pages, membrane paradigm derivation of η/s used, applications on M2-branes and M5-branes added, the title is changed

摘要：

我们重新回顾了具有Einstein引力对偶的强耦合各向同性等离子体的全息剪切粘性张量的膜范式计算，强调了剪切粘性是一个四阶张量这一在以前的文献中被忽略的事实.使用膜范例，我们表明，取决于是否全息剪切粘度张量熵密度比是η^j_i^j_i/s或η^{jiji}/s或η_{jiji}/s，我们可以导出三个不同的公式，全息剪切粘度张量熵密度比明确地给出的背景度量g_{ij}。我们发现，对于各向同性背景度规g_{ij}，广泛研究的全息剪切粘度张量与熵密度比η^j_i^j_i/s取普适值1/（4π），而全息剪切粘度张量与熵密度比η^{jiji}/s和η_{jiji}/s取非普适值，这取决于各向同性背景度规g_{ij}的细节.

英文摘要：

We revisit the membrane paradigm calculations of the holographic shear viscosity tensor of strongly coupled isotropic plasmas with Einstein gravity dual by emphasizing the fact which was overlooked in the previous literatures that the shear viscosity is a fourth-rank tensor. Using the membrane paradigm we show that depending on whether the holographic shear viscosity tensor to entropy density ratio is η^j_i^j_i/s or η^{jiji}/s or η_{jiji}/s, we can derive three distinct formulae for the holographic shear viscosity tensor to entropy density ratios given explicitly in terms of the background metric g_{ij}. We find that the widely studied η^j_i^j_i/s holographic shear viscosity tensor to entropy density ratio takes the universal value 1/(4π) for isotropic background metric g_{ij} but η^{jiji}/s and η_{jiji}/s holographic shear viscosity tensor to entropy density ratios take non-universal values which depend on the details of the isotropic background metric g_{ij}.

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摘要：

英文摘要：

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