Transitions in the Web of Heterotic Vacua

TL;DR

This paper investigates how heterotic string vacua transition between different gauge configurations through geometric and field-theoretic methods, affecting gauge symmetry, spectrum, and invariants on Calabi-Yau manifolds.

Contribution

It introduces a dual approach combining effective field theory and geometry to analyze heterotic vacuum transitions, including explicit solutions for vector bundle deformations.

Findings

Transitions alter gauge symmetry and massless spectrum.

Explicit solutions for rank-changing vector bundle deformations.

Application to Donaldson-Thomas invariants on Calabi-Yau threefolds.

Abstract

We analyze transitions between heterotic vacua with distinct gauge bundles using two complementary methods - the effective four-dimensional field theory and the corresponding geometry. From the viewpoint of effective field theory, such transitions occur between flat directions of the potential energy associated with heterotic stability walls. Geometrically, this branch structure corresponds to smooth deformations of the gauge bundle coupled to the chamber structure of K\"ahler moduli space. We demonstrate how such transitions can change important properties of the effective theory, including the gauge symmetry and the massless spectrum. Geometrically, this study is divided into deformations of the vector bundle which preserve the rank of the gauge bundle and those which change the rank. In the latter case, our results provide explicit solutions to a class of Li-Yau type deformation problems. Finally, we use the framework of stability walls and their effective theory to study Donaldson-Thomas invariants on Calabi-Yau threefolds.