Stability Walls in Heterotic Theories

TL;DR

This paper explores how internal gauge fields in heterotic theories influence the Kahler moduli space, revealing a physical picture of bundle stability and supersymmetry breaking through D-term contributions and symmetry changes.

Contribution

It provides a low-energy effective theory description of supersymmetry breaking and bundle stability transitions in heterotic compactifications.

Findings

Identification of additional anomalous U(1) symmetry at stability transition

Calculation of Kahler-moduli dependent Fayet-Iliopoulos term

Connection between D-term physics and mathematical bundle stability

Abstract

We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilization.