  The in-medium masses of the light vector, $\rho^{0, \pm}$, $\omega$ and the
light axial-vector, $A_1^{0, \pm}$ mesons, are studied in the magnetized
nuclear matter, accounting for the effects of the Dirac sea. The in-medium
partial decay widths for the $A_1\rightarrow \rho \pi$ channels, are studied
from the in-medium masses of the initial and the final state particles, by
applying a phenomenological Lagrangian to account for the $A_1\rho\pi$
interaction vertices. The masses calculated within the QCD sum rule framework,
are obtained in terms of the light quark ($\sim \langle \bar{q}q \rangle$) and
the scalar gluon condensates ($\sim \langle G^2 \rangle$), as well as the light
four-quark condensate ($\sim \langle \bar{q}q\rangle^2 $). The condensates are
calculated within the chiral $SU(3)$ model in terms of the medium modified
scalar fields. The effects of magnetic fields are incorporated through the
Landau energy levels of protons, anomalous magnetic moments (AMMs) of the
nucleons in the nuclear matter, in addition to the magnetized Dirac sea
contribution, within the chiral effective model. The enhancement (reduction) of
the light quark condensates with magnetic field, is called (inverse) magnetic
catalysis. The effects of magnetic fields on the in-medium hadronic decay
widths of the $A_1$ mesons, are observed to be significant through the Dirac
sea effect, accounting for the AMMs of the nucleons. This may affect the light
mesons production in the non-central, heavy-ion collision experiments, where
estimated magnetic field is very large.
