Harmonic metrics for the Hull-Strominger system and stability

TL;DR

This paper introduces a new harmonic metric concept for the Hull-Strominger system, linking stability conditions to solutions and providing examples on the Iwasawa manifold.

Contribution

It develops a harmonic metric framework for the Hull-Strominger system, connecting stability, hyperKähler geometry, and non-Hermitian Yang-Mills connections.

Findings

Harmonic metrics relate to stability conditions for solutions.

Existence of harmonic metrics is expected for generic solution families.

Infinite families of solutions are constructed on the Iwasawa manifold.

Abstract

We investigate stability conditions related to the existence of solutions of the Hull-Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull-Strominger system is recasted using non-Hermitian Yang-Mills connections and holomorphic Courant algebroids. Our main development is a notion of harmonic metric for the Hull-Strominger system, motivated by an infinite-dimensional hyperK\"ahler moment map and related to a numerical stability condition, which we expect to exist generically for families of solutions. We illustrate our theory with an infinite number of continuous families of examples on the Iwasawa manifold.