  Dilepton production from hot, dense and magnetized quark matter is studied
using the 3-flavor Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model in
which the anomalous magnetic moment (AMM) of the quarks is also taken into
consideration. This is done by first evaluating the thermo-magnetic spectral
function of the vector current correlator employing the real time formalism of
finite temperature field theory and the Schwinger proper time formalism. The
constituent quark mass which goes as an input in the expression of the dilepton
production rate (DPR), has been calculated using the 3-flavor PNJL model
employing Pauli-Villiars (PV) regularization. The obtained constituent quark
mass being strongly dependent on the temperature, density, magnetic field and
AMM of the quarks, captures the effect of `strong' interactions specifically
around the (pseudo) chiral and confinement-deconfinement phase transition
regions. The analytic structure of the spectral function in the complex energy
plane has been analyzed in detail and a non-trival Landau cut is found in the
physical kinematic domains resulting from the scattering of the Landau
quantized quark/antiquark with the photon which is purely a finite magnetic
field effect. Due to the emergence of the Landau cut along with the usual
unitary cut, the DPR is found to be largely enhanced in the low invariant mass
region. Owing to the magnetic field and AMM dependence of the thresholds of
these cuts, we find that the kinematically forbidden gap between the Unitary
and Landau cuts vanishes at sufficiently high temperature, density and magnetic
field leading to the generation of a continuous spectrum of dilepton emission
over the whole invariant mass region. In order to see the effects of
strangeness and confinement-deconfinement, the rates are compared with the
3-flavor NJL and the 2-flavor NJL and PNJL models.
