  We suggest the new feature of primordial gravitational waves sourced by the
axion-gauge couplings, whose forms are motivated by the dimensional reduction
of the form field in the string theory.
  In our inflationary model, as an inflaton we adopt two types of axion, dubbed
the model-independent axion and the model-dependent axion, which couple with
two gauge groups with different sign combination each other.
  Due to these forms both polarization modes of gauge fields are amplified and
enhance both helicies of tensor modes during inflation.
  We point out the possibility that a primordial blue-tilted tensor power
spectra with small chirality are provided by the combination of these
axion-gauge couplings, intriguingly both amplitudes and chirality are
potentially testable by future space-based gravitational wave interferometers
such as DECIGO and BBO project.
