Research On Related Issues Of Gravity/Gauge Field Correspondence And Non-Fermi Liquid Theory

Gravity/Gauge field correspondence provides us a powerful tool on studying the strong coupled condensed matter system. In this thesis, we mainly study the non-relativistic limit of holographic non-Fermi liquid, the influence of chemical potential to the dual liquid and holographic anisotropic non-Fermi liquid. In chapter I, we give a brief review on Landau Fermi liquid theory, non-Fermi liquid, AdS/CFT correspon-dence and holographic non-Fermi liquid. In chapter Ⅱ, we investigate the properties of holographic fermions in charged Lifshitz black holes at finite temperature through the AdS/CFT correspondence. We study the the influence of the charge of the bulk fermion. We find the holographic fermions system with z=2is a non-Fermi liquid, and can not effect type of dual liquid by the charge of the bulk fermion. We also find the bigger dynamical exponent z will make Fermi surface more smooth. In chapterⅢ, we explore the properties of the holographic fermions in extremal R-charged black hole background with a running chemical potential, as well as the dipole coupling between fermions and the gauge field in the bulk. We find that although the running chemical potential effect the location of the Fermi surface, it does not change the type of dual liquid at mini-mal dipole coupling. We also study the onset of the Fermi gap and the gap effected by running chemical potential and the dipole coupling. The running chemical potential and the dipole coupling altogether can make the change of the type of the dual liquid. In chapter IV, we investigate the probe holographic fermions by using an anisotropic Einstein-Maxwell-Dilaton-Axion theory. We find the type of dual liquid is non-Fermi liquid and the shape of geometry also influence the shape of Fermi surface. The type of dual liquid can not influence by anisotropy. In the last chapter, we summarize this thesis and make some prospect.