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arXiv 1005.4075hep-thcond-mat.other
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全息术与临界之声

Holography and the sound of criticality

Mohammad Edalati, Juan I. Jottar, Robert G. Leigh

摘要:

利用规范/引力对偶技术,讨论了零温度和有限电荷密度下一类$(2+1)$维强耦合场论中矢量和张量守恒流的声道延迟子,假定它与极值Reissner-Nordström AdS $_4$黑洞是全息对偶的.采用解析和数值相结合的方法,我们确定了耦合引力和电磁扰动的有限动量下的准正规模谱,并讨论了为了使黑洞的准正规频率重现场论谱,规范不变变量(主场)的适当选择.我们讨论了近视界AdS $_{2}$几何在确定边界理论中延迟子低频行为中的作用,并评论了IR中临界性的出现。此外,我们建立了零温度下声模的存在,并数值计算了声速和声衰减常数,获得了与流体力学零温极限预期一致的结果。还研究了高次共振的色散关系。

英文摘要:

Using gauge/gravity duality techniques, we discuss the sound-channel retarded correlators of vector and tensor conserved currents in a class of $(2+1)$-dimensional strongly-coupled field theories at zero temperature and finite charge density, assumed to be holographically dual to the extremal Reissner-Nordström AdS$_4$ black hole. Using a combination of analytical and numerical methods, we determine the quasinormal mode spectrum at finite momentum for the coupled gravitational and electromagnetic perturbations, and discuss the appropriate choice of gauge-invariant variables (master fields) in order for the black hole quasinormal frequencies to reproduce the field theory spectrum. We discuss the role of the near horizon AdS$_{2}$ geometry in determining the low-frequency behavior of retarded correlators in the boundary theory, and comment on the emergence of criticality in the IR. In addition, we establish the existence of a sound mode at zero temperature and compute the speed of sound and sound attenuation constant numerically, obtaining a result consistent with the expectations from the zero temperature limit of hydrodynamics. The dispersion relation of higher resonances is also investigated.

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