Ubiquity of non-geometry in heterotic compactifications

TL;DR

This paper demonstrates that quantum corrections cause most heterotic compactifications on elliptic fibrations to become non-geometric T-folds, revealing a pervasive non-geometry in these string theory models.

Contribution

It shows that quantum effects induce non-geometric T-fold structures in heterotic compactifications, extending previous observations and resolving existing puzzles.

Findings

Most elliptic heterotic compactifications become non-geometric T-folds.

Quantum corrections cause splitting into T-fects with T-duality monodromy.

Subtlety at finite fiber size affects heterotic/F-theory duality analysis.

Abstract

We study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest non-trivial elliptic fibration the effect is quite dramatic: the $I_1$ degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the $T^2$. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety due to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.