Infinite number of MSSMs from heterotic line bundles?

TL;DR

This paper investigates the possibility of infinite heterotic string models with line bundle backgrounds on Calabi-Yau manifolds, finding they are likely unphysical due to constraints from stability conditions and the need for scalar VEVs.

Contribution

It demonstrates that infinite sets of heterotic models with growing flux quanta are at the boundary of physical validity, linking their existence to the failure of stability conditions inside the Kaehler cone.

Findings

Infinite models are at the boundary of the theory's validity.

Stability conditions cannot be satisfied without scalar VEVs.

Such infinite models are unlikely to be realized in exact CFT constructions.

Abstract

We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau manifolds with line bundle gauge backgrounds. Infinite sets of models that satisfy the Bianchi identities and flux quantization conditions can be constructed by letting their background flux quanta grow without bound. Even though we do not have a general proof, we find that all examples are at the boundary of the theory's validity: the Donaldson-Uhlenbeck-Yau equations, which can be thought of as vanishing D-term conditions, cannot be satisfied inside the Kaehler cone unless a growing number of scalar Vacuum Expectation Values (VEVs) is switched on. As they are charged under various line bundles simultaneously, the gauge background gets deformed by these VEVs to a non-Abelian bundle. In general, our physical expectation is that such infinite sets of models should be impossible, since they never seem to occur in exact CFT constructions.