  We investigate the thermal photon production from constant magnetic field in
a strongly coupled and anisotropic plasma via the gauge/gravity duality. The
dual geometry with pressure anisotropy is generated from the axion-dilaton
gravity action introduced by Mateos and Trancancelli and the magnetic field is
coupled to fundamental matters(quarks) through the D3/D7 embeddings. We find
that the photon spectra with different quark mass are enhanced at large
frequency when the photons are emitted parallel to the anisotropic direction
with larger pressure or perpendicular to the magnetic field. However, in the
opposite conditions for the emitted directions, the spectra approximately
saturate isotropic results in the absence of magnetic field. On the other hand,
a resonance emerges at moderate frequency for the photon spectrum with heavy
quarks when the photons move perpendicular to the magnetic field. The resonance
is more robust when the photons are polarized along the magnetic field. On the
contrary, in the presence of pressure anisotropy, the resonance will be
suppressed. There exist competing effects of magnetic field and pressure
anisotropy on meson melting in the strongly coupled super Yang-Mills plasma,
while we argue that the suppression led by anisotropy may not be applied to the
quark gluon plasma.
