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

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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.