Cosmic microwave background bispectrum of vector modes induced from
  primordial magnetic fields
  We calculate the cosmic microwave background bispectrum of vector modes
induced from primordial magnetic fields. We take into account the full angular
dependence of the bispectrum and discuss the amplitude and also the shape of
the bispectrum in $\ell$ space. In the squeezed limit as $\ell_1 = \ell_2 \gg
\ell_3$, we estimate a typical values of the normalized reduced bispectrum as
$\ell_1(\ell_1 + 1)\ell_3(\ell_3+1)|b_{\ell_1\ell_2\ell_3}| \sim 2 \times
10^{-19}$, for the strength of the primordial magnetic field smoothed on $1
{\rm Mpc}$ scale $B_{1 \rm Mpc} = 4.7 \rm nG$ assuming a nearly scale-invariant
spectrum of magnetic fields. We find that a constraint on the magnetic field
strength will be roughly estimated as $B_{1 \rm Mpc} < 10 {\rm nG}$ if PLANCK
places a limit on the nonlinearity parameter of local-type configuration as
$|f^{\rm local}_{\rm NL}| < 5$.
