Analytic formulae of the CMB bispectra generated from non-Gaussianity in
  the tensor and vector perturbations
  We present a complete set of formulae for calculating the bispectra of CMB
temperature and polarization anisotropies generated from non-Gaussianity in the
vector and tensor mode perturbations. In the all-sky analysis it is found that
the bispectrum formulae for the tensor and vector-mode non-Gaussianity formally
take complicated forms compared to the scalar mode one because the photon
transfer functions in the tensor and vector modes depend on the azimuthal angle
between the direction of the wave number vector of the photon's perturbation
and that of the line of sight. We demonstrate that flat-sky approximations
remove this difficulty because this kind of azimuthal angle dependence
apparently vanishes in the flat-sky limit. Through the flat-sky analysis, we
also find that the vector or tensor bispectrum of $B$-mode polarization
vanishes in the squeezed limit, unless the cosmological parity is violated at
the nonlinear level.
