T-dual solutions of the Hull-Strominger system on non-K\"ahler threefolds

TL;DR

This paper constructs new solutions to the Hull-Strominger system on non-K"ahler threefolds, demonstrating T-duality and linking the problem to moduli spaces of stable sheaves on K3 surfaces.

Contribution

It introduces a novel class of solutions on non-K"ahler torus bundles with Hermite-Yang-Mills connections, and establishes T-duality between solutions on different topologies.

Findings

First examples of T-dual solutions on non-K"ahler manifolds.

Reduction of existence problem to moduli spaces of stable sheaves.

Solutions constructed using elementary analytical methods.

Abstract

We construct new examples of solutions of the Hull-Strominger system on non-K\"ahler torus bundles over K3 surfaces, with the property that the connection $\nabla$ on the tangent bundle is Hermite-Yang-Mills. With this ansatz for the connection $\nabla$, we show that the existence of solutions reduces to known results about moduli spaces of slope-stable sheaves on a K3 surface, combined with elementary analytical methods. We apply our construction to find the first examples of T-dual solutions of the Hull-Strominger system on compact non-K\"ahler manifolds with different topology.