The Leading Quantum Corrections to Stringy Kahler Potentials

TL;DR

This work computes the leading quantum corrections to stringy Kahler potentials in weakly coupled heterotic string theory on Calabi–Yau manifolds with non-standard embeddings. By analyzing the ${O}(\alpha'^2)$-corrected ten-dimensional background and performing a detailed KK reduction, the authors derive the four-dimensional Kahler potential for Kahler moduli: $K = -\log {\cal V}' + \frac{\alpha'^2}{2{\cal V}'} \int \tilde h\wedge *\tilde h + O(\alpha'^3)$, where ${\cal V}'$ is the corrected volume and $\tilde h$ encodes moduli-dependent deformations. They show the ${O}(\alpha')$ correction vanishes and establish that the leading quantum correction breaks no-scale structure at ${O}(\alpha'^2)$, in contrast to the extended no-scale behavior found in many Type IIB/F-theory orientifolds where the leading correction cancels in the scalar potential. The results illuminate how higher-dimensional supersymmetry constrains stringy Kahler corrections and have implications for moduli stabilization across duality frames, including mappings to Type I and IIB settings.

Abstract

The structure of stringy quantum corrections to four-dimensional effective theories is particularly interesting for string phenomenology and attempts to stabilize moduli. We consider the heterotic string compactified on a Calabi-Yau space. For this case, we compute the leading corrections to the kinetic terms of moduli fields. The structure of these corrections is largely dictated by the underlying higher-dimensional extended supersymmetry. We find corrections generically of order (alpha')^2 rather than of order (alpha')^3 found in type II compactifications or heterotic compactifications with the standard embedding. We explore the implications of these corrections for breaking no-scale structure.