  In the absence of interactions the conductivity of chiral separation effect
(CSE) in the system of massless fermions is given by topological expression.
Interactions might change the pattern drastically. However, we prove that the
CSE conductivity is still given by the topological invariant composed of the
Green functions at zero temperature as long as the chiral symmetry is present,
and if the renormalized axial current is considered. This allows to predict its
appearance with the standard value of conductivity per Dirac fermion
$\sigma_{CSE} = \frac{1}{2 \pi^2}$ in quark - gluon matter at $T = 0$ and
sufficiently large baryon chemical potential, in the hypothetical phase with
restored chiral symmetry and without color superconductivity. This phase may be
realized inside the neutron stars. We also argue that the same topological
expression for the CSE may be observed in Weyl semimetals, which realize the
system of interacting relativistic fermions in solid state systems. In order to
estimate the non - perturbative corrections to $\sigma_{CSE}$ within QCD at
finite temperatures we apply method of field correlators developed by
Yu.A.Simonov. As expected, above the deconfinement crossover the topological
expression is approached within the quark - gluon plasma phase, when the quark
chemical potential is sufficiently large. However, we observe that this occurs
only when quark chemical potential is much larger than the thermal (Debye)
mass. This range of parameters appears to be far out of the region accessible
at the modern colliders.
