Exact results for metallic quantum critical points
I discuss how exact, non-perturbative results can be obtained for both optical transport and static susceptibilities in “Hertz-Millis” theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, I will show that in the infrared limit, the boson self energy at zero wave vector is a constant independent of frequency, and the real part of the optical conductivity is purely a delta function Drude peak with no other corrections. I will also obtain exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase.