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arXiv 1901.00514hep-th
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具有任意标量非最小耦合的轴荷电黑膜

Axionic charged black branes with arbitrary scalar nonminimal coupling

Adolfo Cisterna, Luis Guajardo, Mokhtar Hassaine

摘要:

本文构造了非最小耦合自作用标量场的四维带电黑膜。除了标量场和麦克斯韦场之外,该模型还包括沿二维平面基流形均匀分布的两个轴子场,从而提供了一种简单的动量耗散机制。有趣的是,解决方案的地平线可以设置在两个不同的位置,其位置取决于axionic参数,在这两种情况下,存在着广泛的非最小耦合参数值产生物理上可接受的解决方案。对于我们的一个解,允许的非最小耦合参数取离散值,并且由于它的温度为零,所以它是极值的。并对解的几何特征进行了全面的分析。最后,根据动量耗散机制,利用黑洞视界数据计算了该解的全息直流电导率,并分析了非最小耦合参数对这些电导率的影响.例如,我们注意到,对于非极值解,总是存在一个非最小耦合(大于四维共形耦合),在电导率无限的意义上产生完美的电导率。更令人惊讶的是,极端解的电导率矩阵具有类似霍尔效应的行为。

英文摘要:

In this paper, we construct four-dimensional charged black branes of a nonminimally coupled and self-interacting scalar field. In addition to the scalar and Maxwell fields, the model involves two axionic fields homogeneously distributed along the two-dimensional planar base manifold providing in turn a simple mechanism of momentum dissipation. Interestingly enough, the horizon of the solution can be set at two different positions, whose locations depend on the axionic parameter, and in both cases there exists a wide range of values of the nonminimal coupling parameter yielding physical acceptable solutions. For one of our solutions, the allowed nonminimal coupling parameters take discrete values and it turns out to be extremal since its has zero temperature. A complete analysis of the thermodynamical features of the solutions is also carried out. Finally, thanks to the mechanism of momentum dissipation, the holographic DC conductivities of the solutions are computed in term of the black hole horizon data, and we analyze the effects of the nonminimal coupling parameter on these conductivities. For example, we notice that for the non extremal solutions, there always exists a nonminimal coupling (which is greater than the conformal one in four dimensions) yielding perfect conductivity in the sense that the conductivity is infinite. Even more astonishing, the conductivity matrix for the extremal solutions has a Hall effect-like behavior.

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