  The nucleon axial-vector coupling constant $g_A$ is studied in the presence
of an external magnetic field, and in dense nuclear environments, to emulate
nuclear matter in magnetars. For this purpose we use QCD finite energy sum
rules for two-current and three-current correlators, the former involving
nucleon-nucleon correlators and the latter involving proton-axial-neutron
currents. As a result, the axial-vector coupling constant decreases both with
baryon density as well as with magnetic field. The axial-vector coupling
evaluated with baryon density near the nuclear density $\rho_0$ leads to
$g_A^*\approx 0.92$. In the presence of magnetic fields $g_A$ decreases in
general, but $g_A^*$ does not show significant changes.
