Towards natural inflation from weakly coupled heterotic string theory
  We propose the natural inflation from the heterotic string theory on
"Swiss-Cheese" Calabi-Yau manifold with multiple $U(1)$ magnetic fluxes. Such
multiple $U(1)$ magnetic fluxes stabilize the same number of the linear
combination of the universal axion and K\"ahler axions and one of the K\"ahler
axions is identified as the inflaton. This axion decay constant can be
determined by the size of one-loop corrections to the gauge kinetic function of
the hidden gauge groups, which leads effectively to the trans-Planckian axion
decay constant consistent with the WMAP, Planck and/or BICEP2 data. During the
inflation, the real parts of the moduli are also stabilized by employing the
nature of the "Swiss-Cheese" Calabi-Yau manifold.
