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arXiv 2009.01340hep-th
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具有动量弛豫的黑膜的全息复杂性

Holographic complexity for black branes with momentum relaxation

Davood Mahdavian Yekta, H. Babaei-Aghbolagh, Komeil Babaei Velni, H. Mohammadzadeh

摘要:

利用“复杂性等于作用量”猜想,研究了由$d + 1$维体时空中的Einstein-Maxwell理论和$d - 1$无质量标量场组成的全息玩具模型(称为Einstein-Maxwell-Axion(EMA)理论)中带电和中性AdS黑膜的作用量增长率.从全息的观点来看,标量场是一个在边界上具有动量弛豫的空间依赖的场论,它与均匀各向同性黑膜是对偶的。我们发现,在惠勒-德威特(WDW)补丁的全息复杂性的增长率饱和相应的劳埃德的界限在后期的时间限制。特别是对于中性AdS黑膜,它将表明,复杂性增长率在后期消失的一个特定值的松弛参数$β_{max}$的黑洞的温度是最小的。然后,我们研究了全息对偶理论在最低温度下的输运性质。在四维时空的k-本质模型中,轴子场动力学项的非线性贡献也被考虑。我们还研究了该模型中双子AdS黑膜的全息复杂性的时间演化。

英文摘要:

We employ the "complexity equals action" conjecture to investigate the action growth rate for the charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in $d + 1$-dimensional bulk spacetime with $d - 1$ massless scalar fields which is called Einstein-Maxwell-Axion (EMA) theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of the holographic complexity within the Wheeler-DeWitt (WDW) patch saturates the corresponding Lloyd's bound at the late time limit. Especially for the neutral AdS black branes, it will be shown that the complexity growth rate at late time vanishes for a particular value of relaxation parameter $β_{max}$ where the temperature of the black hole is minimal. Then, we investigate the transport properties of the holographic dual theory in the minimum temperature. A non-linear contribution of the axion field kinetic term in the context of k-essence model in the four-dimensional spacetime is considered as well. We also study the time evolution of the holographic complexity for the dyonic AdS black branes in this model.

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