Helical Phase Inflation

We show that quadratic inflation can be realized by the phase of a complex field with helicoid potential. Remarkably, this helicoid potential can be simply realized in minimal supergravity. The global U(1) symmetry of the K\"ahler potential introduces a flat direction in the F-term potential and evades the ? problem automatically. So such inflation is technically natural. During inflation the norm of the complex field is strongly stabilized and the phase evolves along a flat helix trajectory. The phase excursion is super-Planckian as required by the Lyth bound, while the norm of the complex field can be suppressed in the sub-Planckian region. This model resolves the contradiction between the strict flat condition for inflation and the dangerous corrections from quantum gravity effects.