Quantum Corrections to Heterotic Moduli Potentials

TL;DR

This work analyzes quantum (α') corrections to the Kähler potential in (0,2) heterotic compactifications and asks whether these corrections—together with non-perturbative superpotentials—can stabilize the overall Calabi–Yau volume at large values, analogously to type IIB large‑volume scenarios. The authors show that, due to Special Hermitian structure, the perturbative dJ∧Ω term vanishes, leaving non-perturbative worldsheet instantons as the primary mechanism for Kähler‑moduli stabilization, with gaugino condensation playing a less favorable role for large volumes. A detailed large‑volume analysis reveals that two Kähler moduli cannot realize a large‑volume minimum, whereas three Kähler moduli can, provided the α' correction enters through a nontrivial, volume‑independent function f(t) of the small moduli ratios. By performing axion minimization and exploring the resulting Kähler sector, the paper demonstrates explicit parametric regimes and even a concrete numerical example where a non-supersymmetric large‑volume minimum exists, highlighting potential phenomenological implications for heterotic string compactifications.

Abstract

In a recent paper, we derived the leading alpha' corrections to the Kahler potentials for moduli in (0,2) heterotic compactifications. In the same spirit as the LARGE volume stabilization scenario for type IIB orientifolds, we examine whether these quantum corrections, together with a combination of tree-level and non-perturbative superpotentials, are sufficient to stabilize the overall volume modulus at large values. This is not a priori obvious, since the corrections we found are of a lower order than those used in the type IIB setting. Nevertheless, we find that stabilizing the volume at (exponentially) large values may be possible (under certain conditions) in these heterotic backgrounds.