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

TL;DR

The work addresses realizing natural inflation with a large tensor-to-scalar ratio in a string-inspired framework by stabilizing moduli in a way that separates the real and imaginary parts of Kähler moduli while keeping axions light. It introduces two anomalous $U(1)$ gauge symmetries to freeze the real parts of the moduli via D-terms and stabilize matter by F-terms, complemented by a racetrack-type superpotential from hidden gaugino condensations. The Kim-Nilles-Pelroso alignment emerges from an approximate $S_2$ exchange symmetry between two Kähler moduli, with a small breaking parameter $c/b$ generating a trans-Planckian effective decay constant $f\approx\frac{2b}{cr}$ for the inflaton direction, while the heavy axion is frozen. The model yields a viable inflationary potential, with $\Lambda^4_{1,2}\sim10^{-8}$ and $f$ of order $\mathcal{O}(10)$, offering a UV-complete route to natural inflation in no-scale SUGRA with moduli stabilization.

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 Kähler 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 Kähler 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 Kähler moduli in our model, and a slightly $S_2$ symmetry breaking leads to the natural inflation with super-Planckian decay constant.