Ultraviolet/infrared mixing in non-Fermi liquids

We study low-energy effective field theories for non-Fermi liquids with Fermi surfaces of general dimensions and co-dimensions. When the dimension of Fermi surface is greater than one, low-energy particle-hole excitations remain strongly coupled with each other across the entire Fermi surface. In this case, even the observables that are local in the momentum space (such as the Green's functions) become dependent on the size of the Fermi surface in singular ways, resulting in an ultraviolet/infrared (UV/IR) mixing. By tuning the dimension and co-dimension of the Fermi surface independently, we find perturbative non-Fermi liquid fixed points controlled by both UV/IR mixing and interactions.