Fractionalized (Weyl-)semi-metals and superconductors in three dimensions

We study three-dimensional semi-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 semi-metals, which can arise in both fermion and boson models. We also propose experiments to detect these fractionalized phases.