Dynamic Critical Scaling of the Holographic Spin Fluctuations

Criticality with strong coupling is described by a theory in the vicinity of a non-Gaussian fixed point. The holographic duality conjectures that a theory at a non-Gaussian fixed point with strong coupling is dual to a gravitational theory. In this paper, we present a holographic theory in treating the strongly coupled critical spin fluctuations in quasi-2-dimension. We show that a universal frequency over temperature scaling law is a rather general property of the critical ac spin susceptibility at strongly coupled limit. Explicit results for the dynamic scaling of spin susceptibility are obtained in large-N and large 't Hooft limit. We argue that such critical scaling are in good agreement with a number of experiments, some of which can not be explained by any perturbative spin-density-wave theory. Our results strongly suggest that the anomalous behavior of non-Fermi liquids in materials is closely related to the spin fluctuations described through the non-Gaussian fixed point. The exotic properties of non-Fermi liquids can be viewed as the Fermi liquids coupling to strongly coupled critical spin fluctuations.