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 Kahler axions and one of the Kahler 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.