Applications of AdS/CFT: CondensedMatter Physics

Abstract

AdS/CFT correspondence(or holography) is a duality between gravitational theory and quantum field theory which are two big branches of modern theoretical physics. Through this non-trivial connection, we have been developed new insights and tools to understand problems especially strongly interacting physical systems. For example, the experimental result of the ratio of the quark-gluon plasma’s entropy and viscosity can be explained through the application of AdS/CFT to quantum chromodynamics.

There has been a lot of developments in the application of AdS/CFT. The applications cover not only quantum chromodynamics but also condensed matter systems. Needs for new theoretical tools to study strongly coupled condensed matters such as cuprates, pnictides, heavy fermions, and so on motivates applications of AdS/CFT to condensed matter systems (AdS/CMT).

Through this thesis, we review works of the AdS/CMT which I study during my Ph.D. student curriculum. Specific topics we will focus on are 1) the linear-T resistivity which is the phenomenon that the resistivity is proportional to the temperature linearly 2) Universal bound of the energy diffusion that a universal bound of the ratio of the energy diffusivity and quantum chaotic observables 3) Pole-skipping which is a phenomenon in a Green’s function capture the energy diffusion bound.