Natural inflation and moduli stabilization in heterotic orbifolds

TL;DR

The paper demonstrates that aligned natural inflation can be consistently embedded in heterotic orbifold compactifications with robust moduli stabilization. By exploiting the modular weight structure and Dedekind η functions, two non-perturbative effects (world-sheet instantons, and optionally gaugino condensation) align two axions from Kähler moduli to yield a trans-Planckian inflaton range while keeping the dilaton and moduli heavy. Two explicit Z6-II mini-landscape benchmarks illustrate SUSY-preserving and SUSY-breaking realizations, respectively, achieving f_eff ≈ 5.7 and n_s ≈ 0.96 with r ≈ 0.03–0.04. The results show that large-field inflation can be compatible with moduli stabilization in heterotic orbifolds, potentially informing future studies on gravitational instantons and phenomenological implications.

Abstract

We study moduli stabilization in combination with inflation in heterotic orbifold compactifications in the light of a large Hubble scale and the favored tensor-to-scalar ratio $r \approx 0.05$. To account for a trans-Planckian field range we implement aligned natural inflation. Although there is only one universal axion in heterotic constructions, further axions from the geometric moduli can be used for alignment and inflation. We argue that such an alignment is rather generic on orbifolds, since all non-perturbative terms are determined by modular weights of the involved fields and the Dedekind $η$ function. We present two setups inspired by the mini-landscape models of the $\mathbb Z_{6-\text{II}}$ orbifold which realize aligned inflation and stabilization of the relevant moduli. One has a supersymmetric vacuum after inflation, while the other includes a gaugino condensate which breaks supersymmetry at a high scale.