  In this paper we study the Chiral Separation Effect by means of
first-principles lattice QCD simulations. For the first time in the literature,
we determine the continuum limit of the associated conductivity using 2+1
flavors of dynamical staggered quarks at physical masses. The results reveal a
suppression of the conductivity in the confined phase and a gradual enhancement
toward the perturbative value for high temperatures. In addition to our
dynamical setup, we also investigate the impact of the quenched approximation
on the conductivity, using both staggered and Wilson quarks. Finally, we
highlight the relevance of employing conserved vector and anomalous axial
currents in the lattice simulations.
