朗道的费米液体理论是上世纪发展起来的基于微扰论的理解大部分金属，半导体等大多数材料的一块理论基石。但是上世纪末的一些发现，例如高温超导和重费米子系统等不能基于费米液体理论来理解。近些年发展起来的量子临界现象的研究被认为和理解这些超出标准费米液体理论的行为有密切的关系，但是这些系统的机制还存在非常大争议，部分的原因来自于我们缺少在强耦合的系统中做计算的可靠方法，特别的，对强耦合磁/自旋系统的处理对理解高温超导和重费米子系统有非常重要的意义。本文尝试将规范引力对偶应用于强耦合临界自旋涨落的计算。通过规范引力对偶方法计算了在有限温度情形下赝矢量自旋算符的两点关联函数和磁/自旋感应率，我们讨论了这方面的计算和现实中铜氧化物超导和重费米子系统在临界区域的性质可能存在的联系。

 

We present a holographic theory of strongly coupled critical spinfluctuations in quasi-2-dimension. We show that a universal frequency over temperature scaling law is a rather general property of the critical ac spinsusceptibility at strongly coupled limit. Explicit results for the dynamicscaling of spin susceptibility are obtained in large-N and large 't Hooft limit, the scaling equals unity at low frequency hydrodynamic limit, and a fractional scaling 2/3 at high frequency relativistic limit. The dc spin susceptibility approaches a universal constant independent to temperature. We argue that such scaling behaviors are in good agreement with a number of experiments and crucial in understanding the anomalous behavior of non-Fermi

liquids. The exotic properties of non-Fermi liquids can be viewed as the Fermi liquids coupling to a strongly coupled critical spin fluctuation.