Kahler Cone Substructure

TL;DR

This work identifies a metric-dependent stability constraint for holomorphic bundles in perturbative heterotic compactifications, showing that the Kahler cone splits into chambers with distinct bundle moduli spaces. It develops a concrete framework based on Mumford-Takemoto stability, slope theory, and the discriminant to locate chamber walls, and links wall crossings to a perturbative enhanced $U(1)$ gauge symmetry via D-term dynamics. The study connects these geometric transitions to string dualities (notably heterotic–IIA perspectives) and proposes a complex-structure invariant reformulation on K3s that relies on metric data rather than a fixed complex structure, with extensions to include a $B$-field. The results illuminate how Kahler moduli control the low-energy spectrum and moduli, offering a bridge between algebraic geometry and perturbative heterotic physics and suggesting directions for generalization to higher dimensions and other gauge groups.

Abstract

To define a consistent perturbative geometric heterotic compactification the bundle is required to satisfy a subtle constraint known as ``stability,'' which depends upon the Kahler form. This dependence upon the Kahler form is highly nontrivial---the Kahler cone splits into subcones, with a distinct moduli space of bundles in each subcone---and has long been overlooked by physicists. In this article we describe this behavior and its physical manifestation.