Fractionalized Metals and Superconductors in Three Dimensions

We study three-dimensional metals with nontrivial correlation functions and fractionalized excitations. We formulate for such states a gauge theory, which also naturally describes the fractional quantization of chiral anomaly. We also study fractional superconductors in this description. This formulation leads to the "three-dimensional chiral Luttinger liquids" and fractionalized Weyl semimetals, which can arise in both fermion and boson models. We also propose experiments to detect these fractionalized phases.