Aligned Natural Inflation and Moduli Stabilization from Anomalous $U(1)$ Gauge Symmetries

TL;DR

This paper proposes a string theory-based model for natural inflation that stabilizes moduli using anomalous U(1) symmetries, achieving a trans-Planckian axion decay constant through axion alignment.

Contribution

It introduces a novel moduli stabilization mechanism with anomalous U(1) symmetries that enables natural inflation with a super-Planckian decay constant.

Findings

Achieves moduli stabilization with separated mass scales for real and imaginary parts.

Realizes axion alignment via approximate S2 symmetry of Kähler moduli.

Demonstrates potential for large tensor-to-scalar ratio in string inflation models.

Abstract

To obtain natural inflation with large tensor-to-scalar ratio in string framework, we need a special moduli stabilization mechanism which can separate the masses of real and imaginary components of K\"ahler moduli at different scales, and achieve a trans-Planckian axion decay constant from sub-Planckian axion decay constants. In this work, we stabilize the matter fields by F-terms and the real components of K\"ahler moduli by D-terms of two anomalous $U(1)_X\times U(1)_A$ symmetries strongly at high scales, while the corresponding axions remain light due to their independence on the Fayet-Iliopoulos (FI) term in moduli stabilization. The racetrack-type axion superpotential is obtained from gaugino condensations of the hidden gauge symmetries $SU(n)\times SU(m)$ with massive matter fields in the bi-fundamental respresentations. The axion alignment via Kim-Nilles-Pelroso (KNP) mechanism corresponds to an approximate $S_2$ exchange symmetry of two K\"ahler moduli in our model, and a slightly $S_2$ symmetry breaking leads to the natural inflation with super-Planckian decay constant.