Nonlinear Effective Field Theory of Fermi Liquids

Abstract : Landau's theory of Fermi liquids is a cornerstone of theoretical physics. I will show how to formulate Fermi liquid theory as an effective field theory of bosonic degrees of freedom, using the mathematical formalism of coadjoint orbits. While at the linear level, this theory reduces to existing multidimensional bosonization approaches, it necessarily features nonlinear corrections that are fixed by the geometry of the Fermi surface. These are crucial to reproduce nonlinear response, such as higher-point functions of currents. The effective field theory framework furthermore systematically parametrizes corrections to Fermi liquid behavior, and provides a computationally advantageous approach for non-Fermi liquids -- strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions.