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arXiv 1606.01142hep-th
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具有变化引力耦合常数的引力对偶中的输运

Transport in a gravity dual with a varying gravitational coupling constant

Antonio M. García-García, Bruno Loureiro, Aurelio Romero-Bermúdez

摘要:

我们研究渐近AdS Brans-Dicke(BD)背景,其中Ricci张量R在径向维度上耦合到标量,作为具有不同耦合常数的金属的有效模型。我们发现,平移不变的背景下,直流电导率$σ_Q$的常规部分偏离爱因斯坦麦克斯韦膨胀(EMD)模型的普遍结果。然而,剪切粘度熵比饱和的Kovtun-Son-Starstellum(KSS)的约束。类似的结果适用于更一般的f(R)引力模型。在四个体积尺寸,我们研究了引力和电磁轴依赖耦合引起的动量弛豫。对于足够强的动量耗散引起的前,最近提出的约束上的直流电导率$σ$违反任何有限的电磁轴子耦合。有趣的是,在四个以上的体积尺寸,强动量弛豫的直流电导率随温度降低的低温极限。与其他具有动量弛豫的重力背景一致,剪切粘滞熵比总是低于KSS界限。数值计算表明,在低温、低频和大动量弛豫的极限下,电导率随频率呈线性增长。我们还表明,即使假设几个通道的动量弛豫,中频的光导系数的模块和论点是不一致的铜氧化物的实验结果。

英文摘要:

We study asymptotically AdS Brans-Dicke (BD) backgrounds, where the Ricci tensor R is coupled to a scalar in the radial dimension, as effective models of metals with a varying coupling constant. We show that, for translational invariant backgrounds, the regular part of the dc conductivity $σ_Q$ deviates from the universal result of Einstein-Maxwell-Dilaton (EMD) models. However, the shear viscosity to entropy ratio saturates the Kovtun-Son-Starinets (KSS) bound. Similar results apply to more general f(R) gravity models. In four bulk dimensions we study momentum relaxation induced by gravitational and electromagnetic axion-dependent couplings. For sufficiently strong momentum dissipation induced by the former, a recently proposed bound on the dc conductivity $σ$ is violated for any finite electromagnetic axion coupling. Interestingly, in more than four bulk dimensions, the dc conductivity for strong momentum relaxation decreases with temperature in the low temperature limit. In line with other gravity backgrounds with momentum relaxation, the shear viscosity to entropy ratio is always lower than the KSS bound. The numerical computation of the optical conductivity reveals a linear growth with the frequency in the limit of low temperature, low frequency and large momentum relaxation. We have also shown that the module and argument of the optical conductivity for intermediate frequencies are not consistent with cuprates experimental results, even assuming several channel of momentum relaxation.

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