  The ongoing and future experiments will measure the B-mode from different sky
coverage and frequency bands, with the potential to reveal non-trivial features
in polarization map. In this work we study the TT, TB, EB and BB correlations
associated with the B-mode polarization of CMB map in models of charged
anisotropic inflation. The model contains a chaotic-type large field complex
inflaton which is charged under the $U(1)$ gauge field. We calculate the
statistical anisotropies generated in the power spectra of the curvature
perturbation, the tensor perturbation and their cross-correlation. It is shown
that the asymmetry in tensor power spectrum is a very sensitive probe of the
gauge coupling. While the level of statistical anisotropy in temperature power
spectrum can be small and satisfy the observational bounds, the interactions
from the gauge coupling can induce large directional dependence in tensor
modes. This will leave interesting anisotropic fingerprints in various
correlations involving the B-mode polarization such as the TB cross-correlation
which may be detected in upcoming Planck polarization data. In addition, the TT
correlation receives an anisotropic contribution from the tensor sector which
naturally decays after $l \gtrsim 100$. We expect that the mechanism of using
tensor sector to induce asymmetry at low $l$ to be generic which can also be
applied to address other low $l$ CMB anomalies.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory