Constraining the Kahler Moduli in the Heterotic Standard Model

TL;DR

This paper investigates how the volume of Calabi-Yau threefolds and vector bundle stability conditions constrain the Kähler moduli space in heterotic string compactifications, focusing on the Heterotic Standard Model.

Contribution

It provides explicit bounds on Kähler moduli for stable vector bundles using extension constructions, with detailed analysis for the Heterotic Standard Model.

Findings

Identifies regions in Kähler moduli space where the visible bundle is stable.

Shows no polarization makes the hidden bundle stable.

Demonstrates the regions can be very small.

Abstract

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kaehler moduli which give rise to realistic compactifications of the strongly coupled heterotic string. When vector bundles are constructed using extensions, we provide simple rules to determine lower and upper bounds to the region of the Kaehler moduli space where such compactifications can exist. We show how small these regions can be, working out in full detail the case of the recently proposed Heterotic Standard Model. More explicitely, we exhibit Kaehler classes in these regions for which the visible vector bundle is stable. On the other hand, there is no polarization for which the hidden bundle is stable.