In this thesis, we study the Chiral Magnetic Effect (CME) and the Chiral Separation Effect (CSE) using lattice QCD simulations. We completely characterize the CSE in QCD using 2+1 simulations of staggered quarks tuned at the physical point. We find that the CSE conductivity is severely suppressed at low temperatures, and experiences a very sharp increase around the QCD crossover transition, reaching the value of massless non-interacting fermions at high temperatures. This is the first non-perturbative calculation of an anomalous transport conductivity in physical QCD. In the case of the CME, we show that this effect is not present in thermal equilibrium, in accordance with Bloch's theorem, both for free fermions and in QCD. We emphasize the crucial role of using a conserved vector current in the study of anomalous transport phenomena on the lattice, and how the use of non-conserved currents is behind non-vanishing results for the CME in equilibrium that can be found in the literature. Finally, we study the interplay between the CME and inhomogeneous magnetic fields, which leads us to find a novel localized CME signal in equilibrium. This does not contradict Bloch's theorem, since the total signal averages to zero when summed over the full volume. This effect is present in physical QCD, showing that a local equilibrium CME signal is possible in the presence of gluonic interactions.
Eduardo Garnacho-Velasco (Mon,) studied this question.