A research on the spatially inhomogeneous effects of AdS/CFT duality

AdS/CFT对偶性现在是理解强耦合凝聚态物理的一个非常有用的工具。在过去的几年中，对具有平移对称或旋转对称的高度对称AdS几何进行了大量的研究。在本研究中，我们通过AdS/CFT对偶性研究了强耦合凝聚态物理，考虑了非均匀或各向异性效应对体几何形状的影响。我首先构造了空间非均匀或各向异性的AdS黑膜解，并研究了其几何性质。我还发现，在探针极限下的微扰范围内，晶格效应不会破坏超导态。此外，我们从黑洞刚性定理的角度研究了umklapp散射对电流的耗散。

The AdS/CFT duality is now an extremely useful tool to understand strongly coupled condensed matter physics.Over the past few years a considerable number of studies have been made on highly symmetric AdS geometries with translational or rotational symmetries. In this research, we investigate the strongly coupled condensed matter physics via AdS/CFT duality by taking into account the effects of inhomogeneous or anisotropic effects on the bulk geometries. I first constructed spatially inhomogenous or anisotropic AdS black brane solutions and investigated the geometric properties.I also found that the lattice effect does not break the superconducting state within the perturbation under the probe limit. Furthermore, we investigated the dissipation of an electric current by umklapp scattering from the perspective of black hole rigidity theorem.