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Condensed matter systems consist of many particles that are the order of 10 to the 23rd power. At the microscopic level, the well-established rules of quantum mechanics govern the dynamics of individual particles. However, it is very challenging to predict the behaviors of a whole system, starting from the microscopic theory. For the past 30 years, it has become clear that collective behaviors are governed by organizing principles that are not manifest from microscopic rules of dynamics. The main goal of my research is to identify new dynamical principles that are behind novel emergent phenomena in critical states of quantum matter such as non-Fermi liquids. I am also interested in the interdisciplinary research areas between condensed matter physics, string theory, and gravitational theory. Recently I have developed the quantum renormalization group in which coupling constants in quantum field theories are promoted to dynamical variables. The quantum renormalization group provides a microscopic connection between general D-dimensional quantum field theories and (D+1)-dimensional quantum theories of gravity as conjectured by the AdS/CFT correspondence. I am trying to use it to better understand quantum field theories, quantum gravity, and the holographic principle.
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