Effective Field Theory for Fermi Liquids and non-Fermi liquids

I will show how to construct an effective field theory describing the bosonic sector of Fermi liquids. While at the linear level, the theory is equivalent to multidimensional bosonization, it necessarily features nonlinear corrections that are fixed by symmetry. These are crucial to reproduce nonlinear response and certain other aspects of Fermi liquid theory phenomenology that are not captured by current bosonization approaches. Studying deformations of this effective field theory produces exact results in the bosonic sector of non-Fermi liquids.