Emergent gauge theory and gravity in condensed matter systems

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It is difficult to understand correlated many-body systems from a first principle calculation due to the huge number of coupled degrees of freedom. However, despite the complexity of the system at the microscopic length scale, the long distance properties can be described by a relatively simple effective theory. Effective theory can serve as a characterization of the many-body state in the sense that different phases are described by different effective theories. Until now, several different phases have been realized in condensed matter systems. They include the Landau Fermi liquid state, the symmetry broken state and the topologically ordered phase of the fractional quantum Hall systems. On the other hand we know that the vacuum of our universe is described by richer effective theories which include gauge theory, general relativity and (possibly) supersymmetry. Therefore one can ask whether these effective theories may also emerge in some condensed matter systems. The objective of this research is to search for new states of condensed matter systems whose long distance properties are characterized by gauge theory, general relativity or supersymmetry.